\[ -a y(x)^n-b x^{\frac {n}{1-n}}+y'(x)=0 \] ✓ Mathematica : cpu = 0.275953 (sec), leaf count = 117
\[\text {Solve}\left [\int _1^{\left (\frac {a x^{-\frac {n}{1-n}}}{b}\right )^{\frac {1}{n}} y(x)}\frac {1}{K[1]^n-\left (\frac {(-1)^n b^{1-n} (n-1)^{-n}}{a}\right )^{\frac {1}{n}} K[1]+1}dK[1]=\int _1^xb K[2]^{\frac {n}{1-n}} \left (\frac {a K[2]^{-\frac {n}{1-n}}}{b}\right )^{\frac {1}{n}}dK[2]+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.432 (sec), leaf count = 61
\[-\left (\int _{\textit {\_b}}^{y \relax (x )}\frac {x^{\frac {n}{n -1}}}{\left (a x \left (n -1\right ) \textit {\_a}^{n}+\textit {\_a} \right ) x^{\frac {n}{n -1}}+b x \left (n -1\right )}d \textit {\_a} \right ) \left (n -1\right )+\ln \relax (x )-c_{1} = 0\]