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