# how to solve a system of integro-differential equations?

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Hewa selman on 19 Dec 2021
Commented: Hewa selman on 20 Dec 2021 Hewa selman on 19 Dec 2021 Hewa selman on 20 Dec 2021
Yes, it is more complicated and I need a code for solve it.
I found the code idsolver, for solving integro differential equations, but I am not sure that it used for the system of integro differential equations too.

John D'Errico on 19 Dec 2021
Edited: John D'Errico on 19 Dec 2021
Last time I checked, int(exp(-t),[-inf,T]) is both trivial to integrate, and yet essentially infinite, for ANY finite value of T. So your system of equation is poorly defined. Do I really need to show this?
syms t T
int(exp(-t),[-inf,T])
ans =
That says your system of equations is not solvable.
Hewa selman on 19 Dec 2021
So if I change it a bit to the following form, can I find a code in Matlab to solve the system of the integro-differential equations?
\frac{dx}{dt}=tx(t)+y(t)+sin(y)\int_{0}^t e^{(t-s)} ds \\
x_{0}=0\\
\frac{dy}{dt}=x(t)+ty(t)+cos(x)\int_{0}^t e^{(t-s)} ds \\
y_{0}=1
With regards