\[ -f(x)+\left (-v^2+x^2+1\right ) y(x)+x^2 y''(x)+3 x y'(x)=0 \] ✓ Mathematica : cpu = 0.228074 (sec), leaf count = 73
\[\left \{\left \{y(x)\to \frac {J_v(x) \int _1^x -\frac {1}{2} \pi f(K[1]) Y_v(K[1]) \, dK[1]+Y_v(x) \int _1^x \frac {1}{2} \pi f(K[2]) J_v(K[2]) \, dK[2]}{x}+\frac {c_1 J_v(x)}{x}+\frac {c_2 Y_v(x)}{x}\right \}\right \}\]
✓ Maple : cpu = 0.049 (sec), leaf count = 53
\[ \left \{ y \left ( x \right ) ={\frac {{{\sl J}_{v}\left (x\right )}{\it \_C2}}{x}}+{\frac {{{\sl Y}_{v}\left (x\right )}{\it \_C1}}{x}}-{\frac {\pi \, \left ( {{\sl J}_{v}\left (x\right )}\int \!{{\sl Y}_{v}\left (x\right )}f \left ( x \right ) \,{\rm d}x-{{\sl Y}_{v}\left (x\right )}\int \!{{\sl J}_{v}\left (x\right )}f \left ( x \right ) \,{\rm d}x \right ) }{2\,x}} \right \} \]