\[ a y(x) y'(x)+f(x)+x y(x) y''(x)+x y'(x)^2=0 \] ✓ Mathematica : cpu = 0.080541 (sec), leaf count = 108
\[\left \{\left \{y(x)\to -\sqrt {2} \sqrt {\int _1^x-K[2]^{-a} \left (c_1+\int _1^{K[2]}f(K[1]) K[1]^{a-1}dK[1]\right )dK[2]+c_2}\right \},\left \{y(x)\to \sqrt {2} \sqrt {\int _1^x-K[2]^{-a} \left (c_1+\int _1^{K[2]}f(K[1]) K[1]^{a-1}dK[1]\right )dK[2]+c_2}\right \}\right \}\] ✓ Maple : cpu = 0.086 (sec), leaf count = 114
\[y \relax (x ) = \frac {\sqrt {2}\, \sqrt {\left (a -1\right ) \left (x^{1-a} \left (\int \frac {x^{a} f \relax (x )}{x}d x \right )+x^{1-a} c_{1}-\left (\int f \relax (x )d x \right )-c_{2}\right )}}{a -1}\]