\[ (n+1) a^{2 n} y(x)^{2 n+1}+y''(x)-y(x)=0 \] ✓ Mathematica : cpu = 0.117806 (sec), leaf count = 47
\[\text {Solve}\left [\int _1^{y(x)}\frac {1}{\sqrt {c_1-K[1]^2 \left (a^{2 n} K[1]^{2 n}-1\right )}}dK[1]{}^2=(x+c_2){}^2,y(x)\right ]\] ✓ Maple : cpu = 0.732 (sec), leaf count = 73
\[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt {-{a}^{2\,n}{{\it \_a}}^{2\,n+2}+{{\it \_a}}^{2}+{\it \_C1}}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{\frac {1}{\sqrt {-{a}^{2\,n}{{\it \_a}}^{2\,n+2}+{{\it \_a}}^{2}+{\it \_C1}}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]