\[ -a^n f(x)^{1-n} g'(x) y(x)^n-\frac {y(x) f'(x)}{f(x)}-f(x) g'(x)+y'(x)=0 \] ✓ Mathematica : cpu = 0.405642 (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 = 0.181 (sec), leaf count = 38
\[\frac {a y \relax (x ) \Phi \left (-\left (\frac {a y \relax (x )}{f \relax (x )}\right )^{n}, 1, \frac {1}{n}\right )}{n f \relax (x )}-a g \relax (x )+c_{1} = 0\]