6.29   ODE No. 1562

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

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

Mathematica: cpu = 1.107641 (sec), leaf count = 140 $$\left\{\{y(x)\to c_1{}_0{F}_3(;\frac{1}{2},1-\frac{n}{2},\frac{n}{2}+1;\frac{x^4}{64})+\frac{1}{8}i{c}_2{x}^2{}_0{F}_3(;\frac{3}{2},\frac{3}{2}-\frac{n}{2},\frac{n}{2}+\frac{3}{2};\frac{x^4}{64})+c_3{\left(\frac{i}{2}\right)}^{-n}\mathrm{\Gamma }(1-n{)}^2({\text{ber}}_{-n}(x){}^2+{\text{bei}}_{-n}(x){}^2)+c_4{\left(\frac{i}{2}\right)}^n\mathrm{\Gamma }(n+1{)}^2({\text{ber}}_n(x){}^2+{\text{bei}}_n(x){}^2)\}\right\}$$

Maple: cpu = 0.187 (sec), leaf count = 93 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_n\left((\frac{1}{2}-\frac{i}{2})\sqrt{2}x\right){\mathit{J}}_n\left((\frac{1}{2}+\frac{i}{2})\sqrt{2}x\right)+\mathit{\_}\mathit{C}\mathit{2}{\mathit{J}}_n\left((\frac{1}{2}-\frac{i}{2})\sqrt{2}x\right){\mathit{Y}}_n\left((\frac{1}{2}+\frac{i}{2})\sqrt{2}x\right)+\mathit{\_}\mathit{C}\mathit{3}{\mathit{Y}}_n\left((\frac{1}{2}-\frac{i}{2})\sqrt{2}x\right){\mathit{J}}_n\left((\frac{1}{2}+\frac{i}{2})\sqrt{2}x\right)+\mathit{\_}\mathit{C}\mathit{4}{\mathit{Y}}_n\left((\frac{1}{2}-\frac{i}{2})\sqrt{2}x\right){\mathit{Y}}_n\left((\frac{1}{2}+\frac{i}{2})\sqrt{2}x\right)\}$$