I have obtained the following coupled system of equations as a solution to a couple of a second order ODE with variable coefficients. I have used the method of variation of parameters and got the following solution, however, I can't decouple them easily. I need to get an explicit solution for each dependent variable.
$$ Y_1(x) = f_1(x) + g_1(x)\int h_1(x)\cdot Y_2(x) dx$$ $$ Y_2(x) = f_2(x) + g_2(x)\int h_2(x)\cdot Y_1(x) dx$$