Solving for variables in symbolic equations

I'm new to symbolic matlab. For a system of equations such as:

z = x - a1 - a2....-ai
da1/dt = k1 a1 + z
da2/dt = k2 a2 + z
...
dai/dt = ki ai + z

where x(t).

Can I use "solve", or some other function, to simply find the equation z as a function of x only, i.e. eliminating a1, a2...ai? Thank you for the help on this very basic question?

[Brian]

k1...ki are parameters or constants. And dai/dt are indeed ode equations. So I just wanted to get rid of the ai variables, resulting in one equation with higher order derivatives of z and x. Can one do that with dsolve, as it's not really an ode solution I want just algebra. Thanks for the help!

[Brian]

Hmmm. I can do it by hand for only a1 an a2, obtaining an equation of the form z'' +z'=x''+x' . I was hoping to find a general form of order i for ai. But maybe matlab can't do it? Algebraically it doesn't seem hard, just cumbersome. ..

[Walter Roberson]

Sigh, you didn't say that x was dependent on t.

[Brian]

Oops, now I've added it ;) Any suggestions?

Answer 1

[Walter Roberson]

If da1/dt is intended to represent differentiation, then No, solve() will not be able to handle that. Instead you would need to use the symbolic routine named "dsolve".

Also, you will not be able to eliminate more variables than you have equations. You asked for z as a function of x only, but you also have the k1, k2, ...ki variables.

[Edit]

You cannot process this algebraically, because z contains all of the ai so dai/dt dependent on all the ai implies all of the ai have unstated integrals of all the other ai.

For example, the three equation case, a1, a2, a3, has the following solution. In the below, C1, C2, C3 are constants of integration, and "i" is sqrt(-1). I doubt you would be able to construct this solution from by solving a single differential equation produced by algebraic manipulation of the three simple expressions you have:

a1(t) = (C3 * (((-1 + k1) * k3 - k1) * k2 - k3 * k1) * exp(((1/3) * i) * (((1/4) * i + (1/4) * 3^(1/2)) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) + (3 * i - i * k2 - i * k3 - i * k1) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3) + (-3^(1/2) + i) * (k2^2 + (-k3 - k1) * k2 + 9 - k3 * k1 + k3^2 + k1^2)) * t / (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3)) + (((-1 + k1) * k3 - k1) * k2 - k3 * k1) * C2 * exp(((1/3) * i) * (((1/4) * i - (1/4) * 3^(1/2)) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) + (3 * i - i * k2 - i * k3 - i * k1) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3) + (3^(1/2) + i) * (k2^2 + (-k3 - k1) * k2 + 9 - k3 * k1 + k3^2 + k1^2)) * t / (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3)) + C1 * (((-1 + k1) * k3 - k1) * k2 - k3 * k1) * exp((2/3) * ((-3/2 + (1/2) * k2 + (1/2) * k1 + (1/2) * k3) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3) + (1/4) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) + k1^2 + (-k3 - k2) * k1 + 9 + k3^2 - k3 * k2 + k2^2) * t / (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3)) - k2 * k3 * x) / (((-1 + k1) * k3 - k1) * k2 - k3 * k1),

a2(t) = (1/3) * (-((1/3) * (k2^2 + (-k3 - k1) * k2 + 9 - k3 * k1 + k3^2 + k1^2) * (k1 - 3 - 2 * k2 + k3) * (1 + i * 3^(1/2)) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3) + (k2^2 + (-k1 + 1 - k3) * k2 + (1 + k1) * k3 - 2 * k1) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) + (-((1/24) * i) * 3^(1/2) - 1/24) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(4/3) + (-1 + i * 3^(1/2)) * ((-k1 + 2 * k2 - k3 + 3) * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 2 * k2^4 + (2 - 4 * k3 - 4 * k1) * k2^3 + (k3^2 + (-3 + 10 * k1) * k3 - 3 * k1 + 12 + k1^2) * k2^2 + (k3^3 + (-5 * k1 - 3) * k3^2 + (-12 - 5 * k1^2 + 12 * k1) * k3 - 3 * k1^2 + k1^3 - 12 * k1 - 36) * k2 + (-k1 + 2) * k3^3 + (-3 * k1 + 4 * k1^2 + 12) * k3^2 + (-k1^3 - 3 * k1^2 - 12 * k1 + 18) * k3 + 2 * k1 * (k1 + 3)^2)) * C3 * (((-1 + k1) * k3 - k1) * k2 - k3 * k1) * exp(((1/3) * i) * ((3 * i - i * k2 - i * k3 - i * k1) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3) + ((1/4) * i + (1/4) * 3^(1/2)) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) + (-3^(1/2) + i) * (k1^2 + (-k3 - k2) * k1 + 9 + k3^2 - k3 * k2 + k2^2)) * t / (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3)) + (((-1 + k1) * k3 - k1) * k2 - k3 * k1) * ((1/3) * (k2^2 + (-k3 - k1) * k2 + 9 - k3 * k1 + k3^2 + k1^2) * (k1 - 3 - 2 * k2 + k3) * (-1 + i * 3^(1/2)) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3) + (-k2^2 + (k1 + k3 - 1) * k2 + (-k1 - 1) * k3 + 2 * k1) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) + (-((1/24) * i) * 3^(1/2) + 1/24) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(4/3) + (1 + i * 3^(1/2)) * ((-k1 + 2 * k2 - k3 + 3) * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 2 * k2^4 + (2 - 4 * k3 - 4 * k1) * k2^3 + (k3^2 + (-3 + 10 * k1) * k3 - 3 * k1 + 12 + k1^2) * k2^2 + (k3^3 + (-5 * k1 - 3) * k3^2 + (-12 - 5 * k1^2 + 12 * k1) * k3 - 3 * k1^2 + k1^3 - 12 * k1 - 36) * k2 + (-k1 + 2) * k3^3 + (-3 * k1 + 4 * k1^2 + 12) * k3^2 + (-k1^3 - 3 * k1^2 - 12 * k1 + 18) * k3 + 2 * k1 * (k1 + 3)^2)) * C2 * exp(((1/3) * i) * ((3 * i - i * k2 - i * k3 - i * k1) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3) + ((1/4) * i - (1/4) * 3^(1/2)) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) + (3^(1/2) + i) * (k1^2 + (-k3 - k2) * k1 + 9 + k3^2 - k3 * k2 + k2^2)) * t / (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3)) - 2 * C1 * (((-1 + k1) * k3 - k1) * k2 - k3 * k1) * (-(1/3) * (k2^2 + (-k3 - k1) * k2 + 9 - k3 * k1 + k3^2 + k1^2) * (k1 - 3 - 2 * k2 + k3) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3) + ((1/2) * k2^2 + (-(1/2) * k1 + 1/2 - (1/2) * k3) * k2 + (1/2 + (1/2) * k1) * k3 - k1) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) + (1/24) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(4/3) + (-k1 + 2 * k2 - k3 + 3) * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 2 * k2^4 + (2 - 4 * k3 - 4 * k1) * k2^3 + (k3^2 + (-3 + 10 * k1) * k3 - 3 * k1 + 12 + k1^2) * k2^2 + (k3^3 + (-5 * k1 - 3) * k3^2 + (-12 - 5 * k1^2 + 12 * k1) * k3 - 3 * k1^2 + k1^3 - 12 * k1 - 36) * k2 + (-k1 + 2) * k3^3 + (-3 * k1 + 4 * k1^2 + 12) * k3^2 + (-k1^3 - 3 * k1^2 - 12 * k1 + 18) * k3 + 2 * k1^3 + 12 * k1^2 + 18 * k1) * exp((2/3) * ((-3/2 + (1/2) * k2 + (1/2) * k1 + (1/2) * k3) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3) + (1/4) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) + k1^2 + (-k3 - k2) * k1 + 9 + k3^2 - k3 * k2 + k2^2) * t / (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3)) - 3 * x * k1 * k3 * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) * (k2 - k3))/((12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) * (((-1 + k1) * k3 - k1) * k2 - k3 * k1) * (k2 - k3)),

a3(t) = (1/3) * (-C3 * (((-1 + k1) * k2 - k1) * k3 - k1 * k2) * (-(1/3) * (k3^2 + (-k2 - k1) * k3 + 9 + k2^2 - k1 * k2 + k1^2) * (k1 - 3 + k2 - 2 * k3) * (1 + i * 3^(1/2)) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3) + (-k3^2 + (k1 + k2 - 1) * k3 + (-k1 - 1) * k2 + 2 * k1) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) + (((1/24) * i) * 3^(1/2) + 1/24) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(4/3) + (-1 + i * 3^(1/2)) * ((k1 - 3 + k2 - 2 * k3) * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) - 2 * k3^4 + (4 * k2 + 4 * k1 - 2) * k3^3 + (-k2^2 + (-10 * k1 + 3) * k2 - k1^2 - 12 + 3 * k1) * k3^2 + (-k2^3 + (5 * k1 + 3) * k2^2 + (12 - 12 * k1 + 5 * k1^2) * k2 + 12 * k1 - k1^3 + 3 * k1^2 + 36) * k3 + (-2 + k1) * k2^3 + (-12 + 3 * k1 - 4 * k1^2) * k2^2 + (-18 + 3 * k1^2 + k1^3 + 12 * k1) * k2 - 2 * k1 * (k1 + 3)^2)) * exp(((1/3) * i) * ((3 * i - i * k2 - i * k3 - i * k1) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3) + ((1/4) * i + (1/4) * 3^(1/2)) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) + (-3^(1/2) + i) * (k1^2 + (-k3 - k2) * k1 + 9 + k3^2 - k3 * k2 + k2^2)) * t / (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3)) + (-(1/3) * (-1 + i * 3^(1/2)) * (k3^2 + (-k2 - k1) * k3 + 9 + k2^2 - k1 * k2 + k1^2) * (k1 - 3 + k2 - 2 * k3) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3) + (k3^2 + (-k1 - k2 + 1) * k3 + (1 + k1) * k2 - 2 * k1) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) + (((1/24) * i) * 3^(1/2) - 1/24) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(4/3) + (1 + i * 3^(1/2)) * ((k1 - 3 + k2 - 2 * k3) * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) - 2 * k3^4 + (4 * k2 + 4 * k1 - 2) * k3^3 + (-k2^2 + (-10 * k1 + 3) * k2 - k1^2 - 12 + 3 * k1) * k3^2 + (-k2^3 + (5 * k1 + 3) * k2^2 + (12 - 12 * k1 + 5 * k1^2) * k2 + 12 * k1 - k1^3 + 3 * k1^2 + 36) * k3 + (-2 + k1) * k2^3 + (-12 + 3 * k1 - 4 * k1^2) * k2^2 + (-18 + 3 * k1^2 + k1^3 + 12 * k1) * k2 - 2 * k1 * (k1 + 3)^2)) * (((-1 + k1) * k2 - k1) * k3 - k1 * k2) * C2 * exp(((1/3) * i) * ((3 * i - i * k2 - i * k3 - i * k1) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3) + ((1/4) * i - (1/4) * 3^(1/2)) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) + (3^(1/2) + i) * (k1^2 + (-k3 - k2) * k1 + 9 + k3^2 - k3 * k2 + k2^2)) * t / (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3)) - 2 * C1 * (((-1 + k1) * k2 - k1) * k3 - k1 * k2) * ((1/3) * (k3^2 + (-k2 - k1) * k3 + 9 + k2^2 - k1 * k2 + k1^2) * (k1 - 3 + k2 - 2 * k3) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3) + (-(1/2) * k3^2 + ((1/2) * k2 + (1/2) * k1 - 1/2) * k3 + (-(1/2) * k1 - 1/2) * k2 + k1) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) - (1/24) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(4/3) + (k1 - 3 + k2 - 2 * k3) * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) - 2 * k3^4 + (4 * k2 + 4 * k1 - 2) * k3^3 + (-k2^2 + (-10 * k1 + 3) * k2 - k1^2 - 12 + 3 * k1) * k3^2 + (-k2^3 + (5 * k1 + 3) * k2^2 + (12 - 12 * k1 + 5 * k1^2) * k2 + 12 * k1 - k1^3 + 3 * k1^2 + 36) * k3 + (-2 + k1) * k2^3 + (-12 + 3 * k1 - 4 * k1^2) * k2^2 + (-18 + 3 * k1^2 + k1^3 + 12 * k1) * k2 - 2 * k1^3 - 18 * k1 - 12 * k1^2) * exp((2/3) * ((-3/2 + (1/2) * k2 + (1/2) * k1 + (1/2) * k3) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3) + (1/4) * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) + k1^2 + (-k3 - k2) * k1 + 9 + k3^2 - k3 * k2 + k2^2) * t / (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(1/3)) - 3 * k2 * x * k1 * (12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) * (k2 - k3))/((12 * ((6 * k3 * k2 - 12 - 3 * k2^2 - 3 * k3^2) * k1^4 + (6 * k2^3 - 6 * k3 * k2^2 + (24 - 6 * k3^2) * k2 + 24 * k3 - 24 + 6 * k3^3) * k1^3 + (-3 * k2^4 - 6 * k3 * k2^3 + (18 * k3^2 - 36) * k2^2 + (36 - 6 * k3^3) * k2 - 36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k1^2 + (6 * k3 * k2^4 + (24 - 6 * k3^2) * k2^3 + (36 - 6 * k3^3) * k2^2 + (6 * k3^4 + 108 - 144 * k3) * k2 + 36 * k3^2 + 108 * k3 + 24 * k3^3) * k1 + (-12 - 3 * k3^2) * k2^4 + (24 * k3 - 24 + 6 * k3^3) * k2^3 + (-36 * k3^2 - 108 - 3 * k3^4 + 36 * k3) * k2^2 + (36 * k3^2 + 108 * k3 + 24 * k3^3) * k2 - 12 * k3^2 * (9 + 2 * k3 + k3^2))^(1/2) + 8 * k1^3 + (-12 * k2 - 12 * k3) * k1^2 + (-12 * k2^2 + 48 * k3 * k2 - 12 * k3^2) * k1 - 216 + 8 * k2^3 + 8 * k3^3 - 12 * k3^2 * k2 - 12 * k3 * k2^2)^(2/3) * (((-1 + k1) * k2 - k1) * k3 - k1 * k2) * (k2 - k3))