I have one fredholm integral equation
$$ y(x)=f(x)+\int_0^1 K_1(x,g(x),t)y(x(t))dt$$
and an integro-differential equation
$$ \frac{dg(x)}{dx}=h(x)+\int_0^1 K_2(x,y(x),t)g(x(t))dt$$.
Are there any methods are available to solve such a system? If so references to literature on the method would be appreciated. If there are not methods available what difficulties inhibit finding a solution? Thanks!