\[ -f(x)+\left (x^2-v^2\right ) y(x)+x^2 y''(x)+x y'(x)=0 \] ✓ Mathematica : cpu = 0.11388 (sec), leaf count = 72
\[\left \{\left \{y(x)\to J_v(x) \int _1^x-\frac {\pi Y_v(K[1]) f(K[1])}{2 K[1]}dK[1]+Y_v(x) \int _1^x\frac {\pi J_v(K[2]) f(K[2])}{2 K[2]}dK[2]+c_1 J_v(x)+c_2 Y_v(x)\right \}\right \}\] ✓ Maple : cpu = 0.059 (sec), leaf count = 49
\[ \left \{ y \left ( x \right ) =-{\frac {{{\sl J}_{v}\left (x\right )}\pi }{2}\int \!{\frac {{{\sl Y}_{v}\left (x\right )}f \left ( x \right ) }{x}}\,{\rm d}x}+{\frac {{{\sl Y}_{v}\left (x\right )}\pi }{2}\int \!{\frac {{{\sl J}_{v}\left (x\right )}f \left ( x \right ) }{x}}\,{\rm d}x}+{{\sl Y}_{v}\left (x\right )}{\it \_C1}+{{\sl J}_{v}\left (x\right )}{\it \_C2} \right \} \]