\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( -{v}^{2}+{x}^{2} \right ) y \left ( x \right ) -f \left ( x \right ) =0} \]
Mathematica: cpu = 0.353045 (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 = 0.015 (sec), leaf count = 50 \[ \left \{ y \left ( x \right ) ={{\sl J}_{v}\left (x\right )}{\it \_C2}+{ {\sl Y}_{v}\left (x\right )}{\it \_C1}-{\frac {\pi }{2} \left ( {{\sl J} _{v}\left (x\right )}\int \!{\frac {{{\sl Y}_{v}\left (x\right )}f \left ( x \right ) }{x}}\,{\rm d}x-{{\sl Y}_{v}\left (x\right )}\int \!{\frac {{ {\sl J}_{v}\left (x\right )}f \left ( x \right ) }{x}}\,{\rm d}x \right ) } \right \} \]