\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -a \left ( y \left ( x \right ) \right ) ^{n}-b{x}^{{\frac {n}{1-n}}}=0} \]
Mathematica: cpu = 116.892343 (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 = 0.156 (sec), leaf count = 61 \[ \left \{ -\int _{{\it \_b}}^{y \left ( x \right ) }\!{1{x}^{{\frac {n}{n- 1}}} \left ( \left ( ax \left ( n-1 \right ) {{\it \_a}}^{n}+{\it \_a} \right ) {x}^{{\frac {n}{n-1}}}+b \left ( n-1 \right ) x \right ) ^{-1}} \,{\rm d}{\it \_a} \left ( n-1 \right ) +\ln \left ( x \right ) -{\it \_C1}=0 \right \} \]
Sage: cpu = 0 (sec), leaf count = 0 \[ \text {Maxima was unable to solve this ODE} \]