\[ y(x) \left (x^2 \left (-f'(x)+f(x)^2+1\right )-x f(x)-v^2\right )+\left (x-2 x^2 f(x)\right ) y'(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0622702 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \left (c_1 J_v(x)+c_2 Y_v(x)\right ) e^{\int _1^x f(K[1]) \, dK[1]}\right \}\right \}\]
✓ Maple : cpu = 0.027 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) =\sqrt {x}{{\rm e}^{-{\frac {1}{2}\int \!{\frac {-2\,xf \left ( x \right ) +1}{x}}\,{\rm d}x}}} \left ( {{\sl Y}_{v}\left (x\right )}{\it \_C2}+{{\sl J}_{v}\left (x\right )}{\it \_C1} \right ) \right \} \]