2.1562   ODE No. 1562

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

$$-(4n^2-1)x^2{y}^{″}(x)+(4n^2-1)x{y}^{\prime }(x)+x^4{y}^{(4)}(x)-4x^{4}y(x)+4x^3{y}^{(3)}(x)=0$$ ✓ Mathematica : cpu = 1.09892 (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 = 0.408 (sec), leaf count = 77

$$\{y\left(x\right)=({\mathit{Y}}_n\left((\frac{1}{2}-\frac{i}{2})\sqrt{2}x\right)\mathit{\_}\mathit{C}\mathit{3}+\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_n\left((\frac{1}{2}-\frac{i}{2})\sqrt{2}x\right)){\mathit{J}}_n\left((\frac{1}{2}+\frac{i}{2})\sqrt{2}x\right)+{\mathit{Y}}_n\left((\frac{1}{2}+\frac{i}{2})\sqrt{2}x\right)({\mathit{Y}}_n\left((\frac{1}{2}-\frac{i}{2})\sqrt{2}x\right)\mathit{\_}\mathit{C}\mathit{4}+\mathit{\_}\mathit{C}\mathit{2}{\mathit{J}}_n\left((\frac{1}{2}-\frac{i}{2})\sqrt{2}x\right))\}$$