Sorry for my incorrect using of "analytical" word (I use it to distiguish from numerical solution; English isn't my native language, sometimes I occasionally use calque from russian words). This is not Cauchy problem, there's no any initial conditions. Just was asked to find solution in form of $y = y(x, C)$ or $F(y,x,C) = 0$.

I tried this way, to find solution of homogeneous equation and then use the "variation of constant" method. It's almost impossible.