ODE No. 1602

$$(n+1)a^{2n}y(x{)}^{2n+1}+y^{″}(x)-y(x)=0$$ ✓ 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]
 

$$\text{Solve}[{\int }_1^{y(x)}\frac{1}{\sqrt{c_1-K[1{]}^2(a^{2n}K[1{]}^{2n}-1)}}dK[1]{}^2=(x+c_2){}^2,y(x)]$$ ✓ 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))
 

$${\int }_{}^{y\left(x\right)}\frac{1}{\sqrt{-a^{2n}{\mathit{\text{\_a}}}^{2n+2}+{\mathit{\text{\_a}}}^2+c_1}}d\mathit{\text{\_a}}-x-c_2=0$$