\[ y'(x)^n-f(x) g(y(x))=0 \] ✓ Mathematica : cpu = 0.0533426 (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 = 0.087 (sec), leaf count = 43
\[\left \{c_{1}+\int _{}^{y \left (x \right )}g \left (\textit {\_a} \right )^{-\frac {1}{n}}d \textit {\_a} +\int _{}^{x}-\left (f \left (\textit {\_a} \right ) g \left (y \left (x \right )\right )\right )^{\frac {1}{n}} g \left (y \left (x \right )\right )^{-\frac {1}{n}}d \textit {\_a} = 0\right \}\]