6.10   ODE No. 1543

$$\boxed{{\displaystyle \mathit{d}\mathit{4}\mathit{y}\left(x\right)-(12k^2{\left(\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(z,x)\right)}^2+a)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+b\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(\alpha {\left(\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(z,x)\right)}^2+\beta )y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.100013 (sec), leaf count = 47 $$\text{DSolve}[-y^{″}(x)(a+12k^2\text{sn}(z|x{)}^2)+y(x)(\alpha \text{sn}(z|x{)}^2+\beta )+b{y}^{\prime }(x)+y^{(4)}(x)=0,y(x),x]$$

Maple: cpu = 5.319 (sec), leaf count = 59 $$\{y\left(x\right)=\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{\frac{{\mathrm{d}}^4}{\mathrm{d}{x}^4}\mathit{\_}\mathit{Y}\left(x\right)+(-12k^2{\left(\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(z,x)\right)}^2-a)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)+b\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)+(\alpha {\left(\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}(z,x)\right)}^2+\beta )\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\}$$