\[ y(x) \left (x^2 \left (-f'(x)+f(x)^2+1\right )-x f(x)-v^2\right )+\left (x-2 x^2 f(x)\right ) y'(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0234528 (sec), leaf count = 42
DSolve[y[x]*(-v^2 - x*f[x] + x^2*(1 + f[x]^2 - Derivative[1][f][x])) + (x - 2*x^2*f[x])*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 J_v(x) \exp \left (\int _1^xf(K[1])dK[1]\right )+c_2 Y_v(x) \exp \left (\int _1^xf(K[1])dK[1]\right )\right \}\right \}\] ✓ Maple : cpu = 0.027 (sec), leaf count = 35
dsolve(x^2*diff(diff(y(x),x),x)+(x-2*x^2*f(x))*diff(y(x),x)+(x^2*(1+f(x)^2-diff(f(x),x))-x*f(x)-v^2)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-\frac {\left (\int \frac {-2 x f \left (x \right )+1}{x}d x \right )}{2}} \sqrt {x}\, \left (c_{1} \BesselJ \left (v , x\right )+c_{2} \BesselY \left (v , x\right )\right )\]