\[ y(x) \left (x^2 \left (a+f'(x)+f(x)^2\right )-(v-1) v\right )+2 x^2 f(x) y'(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 193.502 (sec), leaf count = 96
\[\left \{\left \{y(x)\to c_1 J_{\frac {1}{2} (2 v-1)}\left (\sqrt {a} x\right ) \exp \left (\int _1^x \frac {1-2 K[1] f(K[1])}{2 K[1]} \, dK[1]\right )+c_2 Y_{\frac {1}{2} (2 v-1)}\left (\sqrt {a} x\right ) \exp \left (\int _1^x \frac {1-2 K[1] f(K[1])}{2 K[1]} \, dK[1]\right )\right \}\right \}\]
✓ Maple : cpu = 0.02 (sec), leaf count = 51
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {\int \!2\,f \left ( x \right ) \,{\rm d}x}{2}}}}\sqrt {x}{{\sl J}_{v-{\frac {1}{2}}}\left (\sqrt {a}x\right )}+{\it \_C2}\,{{\rm e}^{-{\frac {\int \!2\,f \left ( x \right ) \,{\rm d}x}{2}}}}\sqrt {x}{{\sl Y}_{v-{\frac {1}{2}}}\left (\sqrt {a}x\right )} \right \} \]