5.13   ODE No. 1461

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)-(3k^2{\left(\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(z,x)\right)}^2+a)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(b+c{\left(\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(z,x)\right)}^2-3k^2\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(z,x)\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{C}\mathit{N}(z,x)\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{D}\mathit{N}(z,x))y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.029504 (sec), leaf count = 55 $$\text{DSolve}[-y^{\prime }(x)(a+3k^2\text{sn}(z|x{)}^2)+y(x)(b+c\text{sn}(z|x{)}^2-3k^2\text{cn}(z|x)\text{dn}(z|x)\text{sn}(z|x))+y^{(3)}(x)=0,y(x),x]$$

Maple: cpu = 1.154 (sec), leaf count = 63 $$\{y\left(x\right)=\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}\mathit{\_}\mathit{Y}\left(x\right)+(-3k^2{\left(\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(z,x)\right)}^2-a)\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)+(b+c{\left(\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(z,x)\right)}^2-3k^2\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(z,x)\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{C}\mathit{N}(z,x)\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{D}\mathit{N}(z,x))\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\}$$