\[ -f(x)+\left (-v^2+x^2+1\right ) y(x)+x^2 y''(x)+3 x y'(x)=0 \] ✓ Mathematica : cpu = 0.065056 (sec), leaf count = 75
\[\left \{\left \{y(x)\to \frac {J_v(x) \int _1^x-\frac {1}{2} \pi Y_v(K[1]) f(K[1])dK[1]+Y_v(x) \int _1^x\frac {1}{2} \pi J_v(K[2]) f(K[2])dK[2]}{x}+\frac {c_1 J_v(x)}{x}+\frac {c_2 Y_v(x)}{x}\right \}\right \}\] ✓ Maple : cpu = 0.067 (sec), leaf count = 49
\[ \left \{ y \left ( x \right ) ={\frac {-{{\sl J}_{v}\left (x\right )}\pi \,\int \!{{\sl Y}_{v}\left (x\right )}f \left ( x \right ) \,{\rm d}x+{{\sl Y}_{v}\left (x\right )}\pi \,\int \!{{\sl J}_{v}\left (x\right )}f \left ( x \right ) \,{\rm d}x+2\,{{\sl Y}_{v}\left (x\right )}{\it \_C1}+2\,{{\sl J}_{v}\left (x\right )}{\it \_C2}}{2\,x}} \right \} \]