\[ -f(x)+\left (x^2-v^2\right ) y(x)+x^2 y''(x)+x y'(x)=0 \] ✓ Mathematica : cpu = 0.127894 (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 = 0.046 (sec), leaf count = 49
\[\left \{y \left (x \right ) = c_{1} \BesselY \left (v , x\right )+c_{2} \BesselJ \left (v , x\right )-\frac {\pi \BesselJ \left (v , x\right ) \left (\int \frac {\BesselY \left (v , x\right ) f \left (x \right )}{x}d x \right )}{2}+\frac {\pi \BesselY \left (v , x\right ) \left (\int \frac {\BesselJ \left (v , x\right ) f \left (x \right )}{x}d x \right )}{2}\right \}\]