\[ (n+1) a^{2 n} y(x)^{2 n+1}+y''(x)-y(x)=0 \] ✓ Mathematica : cpu = 0.135807 (sec), leaf count = 47
DSolve[-y[x] + a^(2*n)*(1 + n)*y[x]^(1 + 2*n) + Derivative[2][y][x] == 0,y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}\frac {1}{\sqrt {c_1-K[1]^2 \left (a^{2 n} K[1]^{2 n}-1\right )}}dK[1]{}^2=(x+c_2){}^2,y(x)\right ]\] ✓ Maple : cpu = 0.257 (sec), leaf count = 73
dsolve(diff(diff(y(x),x),x)+(n+1)*a^(2*n)*y(x)^(2*n+1)-y(x)=0,y(x))
\[\int _{}^{y \left (x \right )}\frac {1}{\sqrt {-a^{2 n} \textit {\_a}^{2 n +2}+\textit {\_a}^{2}+c_{1}}}d \textit {\_a} -x -c_{2} = 0\]