The following ODE is a linear, second-order,non-homogenous equation with variable coefficients. I have tried to get the analytical solution by using the method of Variation of Parameters which in turn requires the solution of the corresponding homogeneous ODE. I can find the solution in Mathematica, but I need to understand the solution steps.
$$ y''(x) + (\frac{a}{x}) y'(x)- (b) y(x) = c$$
Where: $a,b,c$ are constants