\[ y'(x)^n-f(x) g(y(x))=0 \] ✓ Mathematica : cpu = 0.049637 (sec), leaf count = 41
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}g(K[1])^{-1/n}dK[1]\& \right ]\left [\int _1^xf(K[2])^{\frac {1}{n}}dK[2]+c_1\right ]\right \}\right \}\] ✓ Maple : cpu = 0.099 (sec), leaf count = 43
\[\int _{}^{y \relax (x )}g \left (\textit {\_a} \right )^{-\frac {1}{n}}d \textit {\_a} +\int _{}^{x}-\left (f \left (\textit {\_a} \right ) g \left (y \relax (x )\right )\right )^{\frac {1}{n}} g \left (y \relax (x )\right )^{-\frac {1}{n}}d \textit {\_a} +c_{1} = 0\]