\[ y(x) \left (x^2 \left (-f'(x)+f(x)^2+1\right )-x f(x)-v^2\right )+\left (x-2 x^2 f(x)\right ) y'(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0601643 (sec), leaf count = 40
\[\left \{\left \{y(x)\to c_1 J_v(x) e^{\int _1^x f(K[1]) \, dK[1]}+c_2 Y_v(x) e^{\int _1^x f(K[1]) \, dK[1]}\right \}\right \}\]
✓ Maple : cpu = 0.024 (sec), leaf count = 53
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {1}{2}\int \!{\frac {-2\,xf \left ( x \right ) +1}{x}}\,{\rm d}x}}}\sqrt {x}{{\sl J}_{v}\left (x\right )}+{\it \_C2}\,{{\rm e}^{-{\frac {1}{2}\int \!{\frac {-2\,xf \left ( x \right ) +1}{x}}\,{\rm d}x}}}\sqrt {x}{{\sl Y}_{v}\left (x\right )} \right \} \]