\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +3\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( -{v}^{2}+{x}^{2}+1 \right ) y \left ( x \right ) -f \left ( x \right ) =0} \]
Mathematica: cpu = 0.231029 (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 = 0.047 (sec), leaf count = 53 \[ \left \{ y \left ( x \right ) ={\frac {{{\sl J}_{v}\left (x\right )}{\it \_C2}}{x}}+{\frac {{{\sl Y}_{v}\left (x\right )}{\it \_C1}}{x}}+{\frac { \pi \, \left ( {{\sl Y}_{v}\left (x\right )}\int \!{{\sl J}_{v}\left (x \right )}f \left ( x \right ) \,{\rm d}x-{{\sl J}_{v}\left (x\right )}\int \!{{\sl Y}_{v}\left (x\right )}f \left ( x \right ) \,{\rm d}x \right ) }{2 \,x}} \right \} \]