\[ y'(x)^n-f(x) g(y(x))=0 \] ✓ Mathematica : cpu = 0.178343 (sec), leaf count = 39
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} g(K[1])^{-1/n} \, dK[1]\& \right ]\left [\int _1^x f(K[2])^{\frac {1}{n}} \, dK[2]+c_1\right ]\right \}\right \}\]
✓ Maple : cpu = 0.094 (sec), leaf count = 43
\[ \left \{ \int ^{y \left ( x \right ) }\! \left ( g \left ( {\it \_a} \right ) \right ) ^{-{n}^{-1}}{d{\it \_a}}+\int ^{x}\!-{\frac {\sqrt [n]{f \left ( {\it \_a} \right ) g \left ( y \left ( x \right ) \right ) }}{\sqrt [n]{g \left ( y \left ( x \right ) \right ) }}}{d{\it \_a}}+{\it \_C1}=0 \right \} \]