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