6.30   ODE No. 1563

$$\boxed{{\displaystyle x^4\mathit{d}\mathit{4}\mathit{y}\left(x\right)+4x^3\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)-(4n^2-1)x^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-(4n^2-1)x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(-4x^4+4n^2-1)y\left(x\right)=0}}$$

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

Mathematica: cpu = 1.852235 (sec), leaf count = 232 $$\left\{\{y(x)\to \frac{\sqrt[4]{-1}{c}_{2}x{}_0{F}_3(;\frac{3}{2},1-\frac{n}{2},\frac{n}{2}+1;\frac{x^4}{64})}{2\sqrt{2}}-\frac{2(-1{)}^{3/4}\sqrt{2}{c}_1{}_0{F}_3(;\frac{1}{2},\frac{1}{2}-\frac{n}{2},\frac{n}{2}+\frac{1}{2};\frac{x^4}{64})}{x}+c_3(-1{)}^{\frac{1}{4}(1-2n)}{2}^{2n+\frac{1}{2}(2n-1)-1}{x}^{1-2n}{}_0{F}_3(;1-n,1-\frac{n}{2},\frac{3}{2}-\frac{n}{2};\frac{x^4}{64})+c_4(-1{)}^{\frac{1}{4}(2n+1)}{2}^{\frac{1}{2}(-2n-1)-2n-1}{x}^{2n+1}{}_0{F}_3(;\frac{n}{2}+1,\frac{n}{2}+\frac{3}{2},n+1;\frac{x^4}{64})\}\right\}$$

Maple: cpu = 0.110 (sec), leaf count = 83 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x({\left({\mathrm{b}\mathrm{e}\mathrm{r}}_n\left(x\right)\right)}^2+{\left({\mathrm{b}\mathrm{e}\mathrm{i}}_n\left(x\right)\right)}^2)+\mathit{\_}\mathit{C}\mathit{2}x({\left({\mathrm{b}\mathrm{e}\mathrm{r}}_{-n}\left(x\right)\right)}^2+{\left({\mathrm{b}\mathrm{e}\mathrm{i}}_{-n}\left(x\right)\right)}^2)+\mathit{\_}\mathit{C}\mathit{3}x{}_0\text{F}{}_3(;\frac{3}{2},1-\frac{n}{2},1+\frac{n}{2};\frac{x^4}{64})+\frac{\mathit{\_}\mathit{C}\mathit{4}}{x}{}_0\text{F}{}_3(;\frac{1}{2},\frac{1}{2}+\frac{n}{2},\frac{1}{2}-\frac{n}{2};\frac{x^4}{64})\}$$