Solving 7 Differential equations

I want to solve the 7 differential equations which are functions of time for the 7 unknowns. I wanted to find the solutions of the equations:

eo(t)=f1(e_0(t),e_1(t),e_2(t),e_3(t),w_1(t),w_2(t),w_3(t))

e1(t)=f2(e_0(t),e_1(t),e_2(t),e_3(t),w_1(t),w_2(t),w_3(t))

e2(t)=f3(e_0(t),e_1(t),e_2(t),e_3(t),w_1(t),w_2(t),w_3(t))

e3(t)=f4(e_0(t),e_1(t),e_2(t),e_3(t),w_1(t),w_2(t),w_3(t))

w1(t)=f5(e_0(t),e_1(t),e_2(t),e_3(t),w_1(t),w_2(t),w_3(t))

w2(t)=f6(e_0(t),e_1(t),e_2(t),e_3(t),w_1(t),w_2(t),w_3(t))

w3(t)=f7(e_0(t),e_1(t),e_2(t),e_3(t),w_1(t),w_2(t),w_3(t))

I have generated the equations of e0, e1, e2, e3, w1, w2, w3. Now, how do I solve these equations, and which commands are needed?

I need to find the values of e0, e1, e2, e3, w1, w2, w3 and get the numerical value of these with respect to t.

The equations which have to be solved are

e0 = - (e_1(t)*w_1(t))/2 - (e_2(t)*w_2(t))/2 - (e_3(t)*w_3(t))/2

e1 = (e_0(t)*w_1(t))/2 - (e_2(t)*w_3(t))/2 - (e_3(t)*w_2(t))/2

e2 =(e_0(t)*w_2(t))/2 - (e_1(t)*w_3(t))/2 + (e_3(t)*w_1(t))/2

e3 = (e_0(t)*w_3(t))/2 + (e_1(t)*w_2(t))/2 - (e_2(t)*w_1(t))/2

w1 = w_2(t)*(1.98019*e_3(t)*(e_1(t)*w_1(t) + e_2(t)*w_2(t) + e_3(t)*w_3(t)) + 1.980*e_0(t)*(e_0(t)*w_3(t) + e_1(t)*w_2(t) - 1.0*e_2(t)*w_1(t)) - 1.980*e_1(t)*(e_0(t)*w_2(t) - 1.0*e_1(t)*w_3(t) + e_3(t)*w_1(t)) - 1.9801*e_2(t)*(e_2(t)*w_3(t) - 1.0*e_0(t)*w_1(t) + e_3(t)*w_2(t))) - 1.0*w_1(t)*(1.0*e_0(t)*(e_1(t)*w_1(t) + e_2(t)*w_2(t) + e_3(t)*w_3(t)) + 1.0*e_1(t)*(e_2(t)*w_3(t) - 1.0*e_0(t)*w_1(t) + e_3(t)*w_2(t)) - 1.0*e_2(t)*(e_0(t)*w_2(t) - 1.0*e_1(t)*w_3(t) + e_3(t)*w_1(t)) - 1.0*e_3(t)*(e_0(t)*w_3(t) + e_1(t)*w_2(t) - 1.0*e_2(t)*w_1(t))) - 1.0*w_3(t)*(1.0*e_0(t)*(e_0(t)*w_2(t) - 1.0*e_1(t)*w_3(t) + e_3(t)*w_1(t)) - 1.0*e_2(t)*(e_1(t)*w_1(t) + e_2(t)*w_2(t) + e_3(t)*w_3(t)) + 1.0*e_1(t)*(e_0(t)*w_3(t) + e_1(t)*w_2(t) - 1.0*e_2(t)*w_1(t)) + 1.0*e_3(t)*(e_2(t)*w_3(t) - 1.0*e_0(t)*w_1(t) + e_3(t)*w_2(t))) - (63.366*kappa^2*(0.72470*w_1(t) + 0.355*kappa*(2.0*e_0(t)e_1(t)(2.0*e_0(t)*e_3(t) + 2.0*e_1(t)*e_2(t)) + 2.0*e_1(t)e_3(t)(e_0(t)^2 - 1.0*e_1(t)^2 + e_2(t)^2 - 1.0*e_3(t)^2)) - 0.3623*kappa*((e_0(t)^2 + e_1(t)^2 - 1.0*e_2(t)^2 - 1.0*e_3(t)^2)*(e_0(t)^2 - 1.0*e_1(t)^2 + e_2(t)^2 - 1.0*e_3(t)^2) + (2.0*e_0(t)*e_3(t) + 2.0*e_1(t)e_2(t))(2.0*e_0(t)*e_3(t) - 2.0*e_1(t)*e_2(t)))))/(l^5*rho)

w2 = w_3(t)*(0.505*e_1(t)*(e_1(t)*w_1(t) + e_2(t)*w_2(t) + e_3(t)*w_3(t)) - 0.505*e_0(t)*(e_2(t)*w_3(t) - 1.0*e_0(t)*w_1(t) + e_3(t)*w_2(t)) + 0.505*e_2(t)*(e_0(t)*w_3(t) + e_1(t)*w_2(t) - 1.0*e_2(t)*w_1(t)) + 0.505*e_3(t)*(e_0(t)*w_2(t) - 1.0*e_1(t)*w_3(t) + e_3(t)*w_1(t))) - 1.0*w_1(t)*(0.505*e_3(t)*(e_1(t)*w_1(t) + e_2(t)*w_2(t) + e_3(t)*w_3(t)) + 0.505*e_0(t)*(e_0(t)*w_3(t) + e_1(t)*w_2(t) - 1.0*e_2(t)*w_1(t)) - 0.505*e_1(t)*(e_0(t)*w_2(t) - 1.0*e_1(t)*w_3(t) + e_3(t)*w_1(t)) - 0.505*e_2(t)*(e_2(t)*w_3(t) - 1.0*e_0(t)*w_1(t) + e_3(t)*w_2(t))) - 1.0*w_2(t)*(1.0*e_0(t)*(e_1(t)*w_1(t) + e_2(t)*w_2(t) + e_3(t)*w_3(t)) + 1.0*e_1(t)*(e_2(t)*w_3(t) - 1.0*e_0(t)*w_1(t) + e_3(t)*w_2(t)) - 1.0*e_2(t)*(e_0(t)*w_2(t) - 1.0*e_1(t)*w_3(t) + e_3(t)*w_1(t)) - 1.0*e_3(t)*(e_0(t)*w_3(t) + e_1(t)*w_2(t) - 1.0*e_2(t)*w_1(t))) - (32.0*kappa^2*(0.7184*w_2(t) - 0.3592*kappa*(2.0*e_0(t)e_1(t)(e_0(t)^2 + e_1(t)^2 - 1.0*e_2(t)^2 - 1.0*e_3(t)^2) + 2.0*e_1(t)e_3(t)(2.0*e_0(t)*e_3(t) - 2.0*e_1(t)*e_2(t)))))/(l^5*rho)

w3 = w_1(t)*(1.0*e_2(t)*(e_1(t)*w_1(t) + e_2(t)*w_2(t) + e_3(t)*w_3(t)) - 1.0*e_0(t)*(e_0(t)*w_2(t) - 1.0*e_1(t)*w_3(t) + e_3(t)*w_1(t)) + 1.0*e_1(t)*(e_0(t)*w_3(t) + e_1(t)*w_2(t) - 1.0*e_2(t)*w_1(t)) + 1.0*e_3(t)*(e_2(t)*w_3(t) - 1.0*e_0(t)*w_1(t) + e_3(t)w_2(t))) + w_2(t)(1.980*e_0(t)*(e_2(t)*w_3(t) - 1.0*e_0(t)*w_1(t) + e_3(t)*w_2(t)) - 1.980*e_1(t)*(e_1(t)*w_1(t) + e_2(t)*w_2(t) + e_3(t)*w_3(t)) + 1.980*e_2(t)*(e_0(t)*w_3(t) + e_1(t)*w_2(t) - 1.0*e_2(t)*w_1(t)) + 1.980*e_3(t)*(e_0(t)*w_2(t) - 1.0*e_1(t)*w_3(t) + e_3(t)*w_1(t))) - 1.0*w_3(t)*(1.0*e_0(t)*(e_1(t)*w_1(t) + e_2(t)*w_2(t) + e_3(t)*w_3(t)) + 1.0*e_1(t)*(e_2(t)*w_3(t) - 1.0*e_0(t)*w_1(t) + e_3(t)*w_2(t)) - 1.0*e_2(t)*(e_0(t)*w_2(t) - 1.0*e_1(t)*w_3(t) + e_3(t)*w_1(t)) - 1.0*e_3(t)*(e_0(t)*w_3(t) + e_1(t)*w_2(t) - 1.0*e_2(t)*w_1(t))) + (63.366*kappa^2*(0.3551*kappa*((e_0(t)^2 + e_1(t)^2 - 1.0*e_2(t)^2 - 1.0*e_3(t)^2)*(e_0(t)^2 - 1.0*e_1(t)^2 + e_2(t)^2 - 1.0*e_3(t)^2) - 1.0*(2.0*e_0(t)*e_3(t) + 2.0*e_1(t)e_2(t))(2.0*e_0(t)*e_3(t) - 2.0*e_1(t)*e_2(t))) - 0.724*w_3(t) + 0.362*kappa*((e_0(t)^2 + e_1(t)^2 - 1.0*e_2(t)^2 - 1.0*e_3(t)^2)*(e_0(t)^2 - 1.0*e_1(t)^2 + e_2(t)^2 - 1.0*e_3(t)^2) + (2.0*e_0(t)*e_3(t) + 2.0*e_1(t)e_2(t))(2.0*e_0(t)*e_3(t) - 2.0*e_1(t)*e_2(t)))))/(l^5*rho)

I used this code in MATLAB after assigning the values

soll=ode45(e0,e1,e2,e3,w1,w2,w3,e_0(t),e_1(t),e_2(t),e_3(t),w_1(t),w_2(t),w_3(t)) But I got the following error message:

Undefined function 'exist' for input arguments of type 'sym'.

Error in odearguments (line 59) if (exist(ode)==2)

Error in ode45 (line 113) [neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

Which solver must i use to solve this equation Please enlighten me where I have gone wrong.

[Torsten]

I don't see any time differentials in your equations - so why using ODE45 ?

Write your (differential ?) equations in a mathematical notation. Then someone might be able to help.

Best wishes

Torsten.