\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{n}-f \left ( x \right ) g \left ( y \left ( x \right ) \right ) =0} \]
Mathematica: cpu = 0.164021 (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 = 0.062 (sec), leaf count = 43 \[ \left \{ \int ^{y \left ( x \right ) }\! \left ( g \left ( {\it \_a} \right ) \right ) ^{-{n}^{-1}}{d{\it \_a}}+\int ^{x}\!-{\frac {\sqrt [ n]{f \left ( {\it \_a} \right ) g \left ( y \left ( x \right ) \right ) }}{ \sqrt [n]{g \left ( y \left ( x \right ) \right ) }}}{d{\it \_a}}+{\it \_C1}=0 \right \} \]