4.27   ODE No. 1027

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-(n(n+1)k^2{\left(\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(x,k)\right)}^2+b)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.995126 (sec), leaf count = 23 $$\text{DSolve}[y(x)(a\text{sn}(x|k{)}^2+b)+y^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.265 (sec), leaf count = 69 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{G}(k^{-2},\frac{b}{4k^2},-\frac{n}{2},\frac{n}{2}+\frac{1}{2},\frac{1}{2},\frac{1}{2},{\left(\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(x,k)\right)}^2)+\mathit{\_}\mathit{C}\mathit{2}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{G}(k^{-2},\frac{k^2+b+1}{4k^2},\frac{n}{2}+1,-\frac{n}{2}+\frac{1}{2},\frac{3}{2},\frac{1}{2},{\left(\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(x,k)\right)}^2)\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(x,k)\}$$