2.1441   ODE No. 1441

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

$$y^{″}(x)=-\frac{y^{\prime }(x)(-\text{cn}(x|k)\text{dn}(x|k)-2\text{sn}(x|k))}{\text{sn}(x|k{)}^2-\text{sn}(a|k{)}^2}-\frac{y(x)(6k^2\text{sn}(a|k{)}^4-4(k^2+1)\text{sn}(a|k{)}^2+2)}{\text{sn}(x|k{)}^2-\text{sn}(a|k{)}^2}-\frac{1}{\text{sn}(x|k{)}^2-\text{sn}(a|k{)}^2}$$ ✗ Mathematica : cpu = 1.0719 (sec), leaf count = 0 , could not solve

DSolve[Derivative[2][y][x] == -(-JacobiSN[a, k]^2 + JacobiSN[x, k]^2)^(-1) - ((2 - 4*(1 + k^2)*JacobiSN[a, k]^2 + 6*k^2*JacobiSN[a, k]^4)*y[x])/(-JacobiSN[a, k]^2 + JacobiSN[x, k]^2) - ((-(JacobiCN[x, k]*JacobiDN[x, k]) - 2*JacobiSN[x, k])*Derivative[1][y][x])/(-JacobiSN[a, k]^2 + JacobiSN[x, k]^2), y[x], x]

✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol

$$\{y\left(x\right)=\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)-2\frac{\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(x,k)\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{C}\mathit{N}(x,k)\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{D}\mathit{N}(x,k)\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)}{{\left(\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(x,k)\right)}^2-\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(a,k)}-\frac{(-2+4(k^2+1){\left(\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(a,k)\right)}^2-6k^2{\left(\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(a,k)\right)}^4)\mathit{\_}\mathit{Y}\left(x\right)}{{\left(\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(x,k)\right)}^2-\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(a,k)}\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\}$$