\[ y(x) \left (x^2 \left (a+f'(x)+f(x)^2\right )+(1-v) v\right )+2 x^2 f(x) y'(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0477669 (sec), leaf count = 98
\[\left \{\left \{y(x)\to c_1 J_{\frac {1}{2} (2 v-1)}\left (\sqrt {a} x\right ) \exp \left (\int _1^x\frac {1-2 f(K[1]) K[1]}{2 K[1]}dK[1]\right )+c_2 Y_{\frac {1}{2} (2 v-1)}\left (\sqrt {a} x\right ) \exp \left (\int _1^x\frac {1-2 f(K[1]) K[1]}{2 K[1]}dK[1]\right )\right \}\right \}\] ✓ Maple : cpu = 0.019 (sec), leaf count = 40
\[\left \{y \left (x \right ) = \left (c_{1} \BesselJ \left (v -\frac {1}{2}, \sqrt {a}\, x \right )+c_{2} \BesselY \left (v -\frac {1}{2}, \sqrt {a}\, x \right )\right ) \sqrt {x}\, {\mathrm e}^{-\frac {\left (\int 2 f \left (x \right )d x \right )}{2}}\right \}\]