\[ b y(x) f(x)^{2 a}-\frac {a f'(x) y'(x)}{f(x)}+y''(x)=0 \] ✓ Mathematica : cpu = 0.207405 (sec), leaf count = 315
\[\left \{\left \{y(x)\to -\frac {\sqrt {c_1} \exp \left (-\int _1^x-i \sqrt {b} f(K[1])^adK[1]-c_2\right ) \left (-1+\exp \left (2 \int _1^x-i \sqrt {b} f(K[1])^adK[1]+2 c_2\right )\right )}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {c_1} \exp \left (-\int _1^x-i \sqrt {b} f(K[1])^adK[1]-c_2\right ) \left (-1+\exp \left (2 \int _1^x-i \sqrt {b} f(K[1])^adK[1]+2 c_2\right )\right )}{\sqrt {2}}\right \},\left \{y(x)\to -\frac {\sqrt {c_1} \exp \left (-\int _1^xi \sqrt {b} f(K[2])^adK[2]-c_2\right ) \left (-1+\exp \left (2 \int _1^xi \sqrt {b} f(K[2])^adK[2]+2 c_2\right )\right )}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {c_1} \exp \left (-\int _1^xi \sqrt {b} f(K[2])^adK[2]-c_2\right ) \left (-1+\exp \left (2 \int _1^xi \sqrt {b} f(K[2])^adK[2]+2 c_2\right )\right )}{\sqrt {2}}\right \}\right \}\] ✓ Maple : cpu = 0.027 (sec), leaf count = 37
\[y \relax (x ) = c_{1} {\mathrm e}^{\int i f \relax (x )^{a} \sqrt {b}d x}+c_{2} {\mathrm e}^{-\left (\int i f \relax (x )^{a} \sqrt {b}d x \right )}\]