\[ y(x) \left (x^2 \left (a+f'(x)+f(x)^2\right )+(1-v) v\right )+2 x^2 f(x) y'(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0442464 (sec), leaf count = 98
DSolve[y[x]*((1 - v)*v + x^2*(a + f[x]^2 + Derivative[1][f][x])) + 2*x^2*f[x]*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 J_{\frac {1}{2} (2 v-1)}\left (\sqrt {a} x\right ) \exp \left (\int _1^x\frac {1-2 f(K[1]) K[1]}{2 K[1]}dK[1]\right )+c_2 Y_{\frac {1}{2} (2 v-1)}\left (\sqrt {a} x\right ) \exp \left (\int _1^x\frac {1-2 f(K[1]) K[1]}{2 K[1]}dK[1]\right )\right \}\right \}\] ✓ Maple : cpu = 0.021 (sec), leaf count = 40
dsolve(x^2*diff(diff(y(x),x),x)+2*x^2*f(x)*diff(y(x),x)+(x^2*(diff(f(x),x)+f(x)^2+a)-v*(v-1))*y(x)=0,y(x))
\[y \left (x \right ) = \sqrt {x}\, {\mathrm e}^{-\frac {\left (\int 2 f \left (x \right )d x \right )}{2}} \left (\BesselY \left (v -\frac {1}{2}, \sqrt {a}\, x \right ) c_{2}+\BesselJ \left (v -\frac {1}{2}, \sqrt {a}\, x \right ) c_{1}\right )\]