\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( n+1 \right ) {a}^{2\,n} \left ( y \left ( x \right ) \right ) ^{2\,n+1}-y \left ( x \right ) =0} \]
Mathematica: cpu = 81.621865 (sec), leaf count = 46 \[ \text {Solve}\left [\left (\int _1^{y(x)} \frac {1}{\sqrt {c_1-K[1]^2 \left (a^{2 n} K[1]^{2 n}-1\right )}} \, dK[1]\right ){}^2=\left (c_2+x\right ){}^2,y(x)\right ] \]
Maple: cpu = 0.125 (sec), leaf count = 73 \[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt {-{a}^{2\,n}{{ \it \_a}}^{2\,n+2}+{{\it \_a}}^{2}+{\it \_C1}}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{\frac {1}{\sqrt {-{a}^{2\,n}{{ \it \_a}}^{2\,n+2}+{{\it \_a}}^{2}+{\it \_C1}}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]