\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( x-2\,{x}^{2}f \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( {x}^{2} \left ( 1+ \left ( f \left ( x \right ) \right ) ^{2}-{\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) -xf \left ( x \right ) -{v}^{2} \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.061508 (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 = 0.016 (sec), leaf count = 53 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {1}{2}\int \!{\frac {-2\,xf \left ( x \right ) +1}{x}}\,{\rm d}x}}}\sqrt {x}{ {\sl J}_{v}\left (x\right )}+{\it \_C2}\,{{\rm e}^{-{\frac {1}{2}\int \! {\frac {-2\,xf \left ( x \right ) +1}{x}}\,{\rm d}x}}}\sqrt {x}{{\sl Y} _{v}\left (x\right )} \right \} \]