How to express constants of integral

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kk123k
kk123k 2025-5-16
评论： Sam Chak 2025-5-16
Ran in:
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 = 
  2 个评论
Torsten
Torsten 2025-5-16
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
kk123k 2025-5-16
I'm sorry. I explained it wrong
How can express C1 and C2 in simplify(u) ?
The answer i want is
C1 +
C2+

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采纳的回答

Torsten
Torsten 2025-5-16
移动：Sam Chak 2025-5-16
Ran in:
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 = 
  4 个评论
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Sam Chak
Sam Chak 2025-5-16
@kk123k, If you find the solution using 'dsolve()' helpful, please consider clicking 'Accept' ✔ on the answer.

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