When I do the product, this ODE doesn't have solution I think that i am doing something wrong. The exercise is:
Use Fourier Series for approach the solution of the ODE $$f'(x)=1+xf(x)$$ for $$0<x< \pi$$
With $$f(0)=f(\pi)=0$$
I proposed $$f(x)=a_nSen(nx)$$ as function but i have problems with the products.