\[ -a y(x)^n-b x^{\frac {n}{1-n}}+y'(x)=0 \] ✓ Mathematica : cpu = 173.409 (sec), leaf count = 115
\[\text {Solve}\left [\int _1^{y(x) \left (\frac {a x^{-\frac {n}{1-n}}}{b}\right )^{\frac {1}{n}}} \frac {1}{-K[1] \left (\frac {(-1)^n (n-1)^{-n} b^{1-n}}{a}\right )^{\frac {1}{n}}+K[1]^n+1} \, dK[1]=\int _1^x b K[2]^{\frac {n}{1-n}} \left (\frac {a K[2]^{-\frac {n}{1-n}}}{b}\right )^{\frac {1}{n}} \, dK[2]+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.406 (sec), leaf count = 61
\[ \left \{ -\int _{{\it \_b}}^{y \left ( x \right ) }\!{1{x}^{{\frac {n}{n-1}}} \left ( \left ( ax \left ( n-1 \right ) {{\it \_a}}^{n}+{\it \_a} \right ) {x}^{{\frac {n}{n-1}}}+b \left ( n-1 \right ) x \right ) ^{-1}}\,{\rm d}{\it \_a} \left ( n-1 \right ) +\ln \left ( x \right ) -{\it \_C1}=0 \right \} \]