\[ -a^n f(x)^{1-n} g'(x) y(x)^n-\frac {y(x) f'(x)}{f(x)}-f(x) g'(x)+y'(x)=0 \] ✓ Mathematica : cpu = 0.30637 (sec), leaf count = 74
\[\text {Solve}\left [y(x) \left (a^n f(x)^{-n}\right )^{\frac {1}{n}} \, _2F_1\left (1,\frac {1}{n};1+\frac {1}{n};-\left (\left (a^n f(x)^{-n}\right )^{\frac {1}{n}} y(x)\right )^n\right )=f(x) g(x) \left (a^n f(x)^{-n}\right )^{\frac {1}{n}}+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.152 (sec), leaf count = 38
\[ \left \{ {\frac {ay \left ( x \right ) }{nf \left ( x \right ) }{\it LerchPhi} \left ( - \left ( {\frac {ay \left ( x \right ) }{f \left ( x \right ) }} \right ) ^{n},1,{n}^{-1} \right ) }-ag \left ( x \right ) +{\it \_C1}=0 \right \} \]