\[ b y(x) f(x)^{2 a}-\frac {a f'(x) y'(x)}{f(x)}+y''(x)=0 \] ✓ Mathematica : cpu = 0.203059 (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 = 0.092 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{\int \!i \left ( f \left ( x \right ) \right ) ^{a}\sqrt {b}\,{\rm d}x}}+{\it \_C2}\,{{\rm e}^{-\int \!i \left ( f \left ( x \right ) \right ) ^{a}\sqrt {b}\,{\rm d}x}} \right \} \]