\[ -f(x)+\left (x^2-v^2\right ) y(x)+x^2 y''(x)+x y'(x)=0 \] ✓ Mathematica : cpu = 0.344402 (sec), leaf count = 70
\[\left \{\left \{y(x)\to J_v(x) \int _1^x -\frac {\pi f(K[1]) Y_v(K[1])}{2 K[1]} \, dK[1]+Y_v(x) \int _1^x \frac {\pi f(K[2]) J_v(K[2])}{2 K[2]} \, dK[2]+c_1 J_v(x)+c_2 Y_v(x)\right \}\right \}\]
✓ Maple : cpu = 0.046 (sec), leaf count = 50
\[ \left \{ y \left ( x \right ) ={{\sl J}_{v}\left (x\right )}{\it \_C2}+{{\sl Y}_{v}\left (x\right )}{\it \_C1}-{\frac {\pi }{2} \left ( {{\sl J}_{v}\left (x\right )}\int \!{\frac {{{\sl Y}_{v}\left (x\right )}f \left ( x \right ) }{x}}\,{\rm d}x-{{\sl Y}_{v}\left (x\right )}\int \!{\frac {{{\sl J}_{v}\left (x\right )}f \left ( x \right ) }{x}}\,{\rm d}x \right ) } \right \} \]