\[ a y(x) y'(x)+f(x)+x y(x) y''(x)+x y'(x)^2=0 \] ✓ Mathematica : cpu = 0.0930389 (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 = 0.115 (sec), leaf count = 114
\[\left \{y \left (x \right ) = \frac {\sqrt {2}\, \sqrt {\left (a -1\right ) \left (c_{1} x^{-a +1}+x^{-a +1} \left (\int \frac {x^{a} f \left (x \right )}{x}d x \right )-c_{2}-\left (\int f \left (x \right )d x \right )\right )}}{a -1}, y \left (x \right ) = -\frac {\sqrt {2}\, \sqrt {\left (a -1\right ) \left (c_{1} x^{-a +1}+x^{-a +1} \left (\int \frac {x^{a} f \left (x \right )}{x}d x \right )-c_{2}-\left (\int f \left (x \right )d x \right )\right )}}{a -1}\right \}\]