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# How to solve this ODE system which involves these integrals?

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Elia Paini on 7 May 2021
Edited: Elia Paini on 7 May 2021
Hi, I'm trying to solve the following (simplified) ODE system (see attached file).
Where X1 and X2 are my functions, z is the integration variable and f1,g1,f2,g2 are 4 different functions of X1 and X2.
My biggest problem is that the integrals depend on the integration variable itself.
I tried to consider z as a symbolic variable in this way:
syms z
integral(f(X1,X2), [0,z])
but I got an error.
Thank you!
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Elia Paini on 7 May 2021
Sorry, was z

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### Accepted Answer

Jan on 7 May 2021
What about using two further variables?
function dx = fcn(z, x)
dx = [f1(x(1), x(2)) / x(3); ...
f2(x(1), x(2)) / x(4); ...
g1(x(1), x(2)); ...
g2(x(1), x(2))];
end
This does calculate the integral from 0 to the current z over g1(x1,x2) already.
##### 1 CommentShowHide None
Elia Paini on 7 May 2021
You're a genius, thank you!

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