\[ -f(x)+\left (-v^2+x^2+1\right ) y(x)+x^2 y''(x)+3 x y'(x)=0 \] ✓ Mathematica : cpu = 0.065767 (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 = 0.065 (sec), leaf count = 49
\[\left \{y \left (x \right ) = \frac {2 c_{1} \BesselY \left (v , x\right )+2 c_{2} \BesselJ \left (v , x\right )-\pi \BesselJ \left (v , x\right ) \left (\int \BesselY \left (v , x\right ) f \left (x \right )d x \right )+\pi \BesselY \left (v , x\right ) \left (\int \BesselJ \left (v , x\right ) f \left (x \right )d x \right )}{2 x}\right \}\]