2.1027   ODE No. 1027

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

$$y(x)(a\text{sn}(x|k{)}^2+b)+y^{″}(x)=0$$ ✗ Mathematica : cpu = 1.28291 (sec), leaf count = 0 , could not solve

DSolve[(b + a*JacobiSN[x, k]^2)*y[x] + Derivative[2][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.408 (sec), leaf count = 69

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