How to express constants of integral

Hi everyone,

I am a matlab beginner. How can I find the constants of integral C1 and C2 ?

For example i know that, how can i find constants of integral C1 and C2 in this script? Thanks :)

syms x
y1 = exp(-2*x+sqrt(6)*x);
y2 = exp(-2*x-sqrt(6)*x);
g = 2*x^2-3*x+6;
A = [y1 y2;diff(y1,x) diff(y2,x)]

A = 

b = [0; g]

b = 

A\b

ans = 

u = simplify(A\b)

u = 

u = int(u,x)

u = 

simplify(u)

ans = 

[Torsten]

What is C1 and C2 in your script ? If you mean the 2x1 vector u: there are no constants because of the multiplication by the exp(...) term.

[kk123k]

I'm sorry. I explained it wrong

How can express C1 and C2 in simplify(u) ?

The answer i want is

C1 +

C2+

Answer 1

[Torsten]

MATLAB's "int" only returns one possible antiderivative.

If you want to show the free integration constants, you could use "dsolve" which is usually used for the symbolic solution of more complicated ordinary differential equations:

syms x
y1 = exp(-2*x+sqrt(6)*x);
y2 = exp(-2*x-sqrt(6)*x);
g = 2*x^2-3*x+6;
A = [y1 y2;diff(y1,x) diff(y2,x)]

A = 

b = [0; g]

b = 

A\b

ans = 

u = simplify(A\b)

u = 

syms v1(x) v2(x)
v(x) = [v1(x);v2(x)];
u = dsolve(diff(v,x)==u);
simplify(u.v1)

ans = 

●

simplify(u.v2)

ans = 

[William Rose]

@Torsten, very impressive.

[Torsten]

@William Rose A lot of formalism for little return :-)

[kk123k]

Thank you ! :)

[Sam Chak]

@kk123k, If you find the solution using 'dsolve()' helpful, please consider clicking 'Accept' ✔ on the answer.