To solve a system of Integro-Differential Equations (IDEs) in Mathematica, one effective approach is to start with a simpler equation, such as y'(x) = 2 - 1/4 x^2 + 1/4∫_0^x y(t) dt, with the initial condition y(0) = 0. A modified Euler method can be employed, where at each time step, the integral ∫_0^{x_k} y(t) dt is computed numerically using values of y(t) from previous calculations. This method allows for the integration of the IDE into the numerical solution process. Although Mathematica lacks built-in commands specifically for IDEs, there are community-developed numerical methods available. After mastering the simpler case, users can progress to more complex systems.
