2.1602   ODE No. 1602

1. Problem in Latex
2. Mathematica input
3. Maple input

$$(n+1)a^{2n}y(x{)}^{2n+1}+y^{″}(x)-y(x)=0$$ ✓ Mathematica : cpu = 86.5668 (sec), leaf count = 46

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

✓ Maple : cpu = 0.28 (sec), leaf count = 73

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