\[ y(x) \left (x^2 \left (a+f'(x)+f(x)^2\right )-(v-1) v\right )+2 x^2 f(x) y'(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 200.107 (sec), leaf count = 61
\[\left \{\left \{y(x)\to \left (c_1 J_{v-\frac {1}{2}}\left (\sqrt {a} x\right )+c_2 Y_{v-\frac {1}{2}}\left (\sqrt {a} x\right )\right ) e^{\int _1^x \left (\frac {1}{2 K[1]}-f(K[1])\right ) \, dK[1]}\right \}\right \}\]
✓ Maple : cpu = 0.02 (sec), leaf count = 40
\[ \left \{ y \left ( x \right ) =\sqrt {x}{{\rm e}^{-{\frac {\int \!2\,f \left ( x \right ) \,{\rm d}x}{2}}}} \left ( {{\sl Y}_{v-{\frac {1}{2}}}\left (\sqrt {a}x\right )}{\it \_C2}+{{\sl J}_{v-{\frac {1}{2}}}\left (\sqrt {a}x\right )}{\it \_C1} \right ) \right \} \]