4.362   ODE No. 1362

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

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

Mathematica: cpu = 14.232807 (sec), leaf count = 115 $$\text{left {left {y(x)to text {DifferentialRoot}left ({unicode {f818},unicode {f817}}unicode {f4a1}left {-2 unicode {f818}'(unicode {f817}) unicode {f817}^3+left (a^2 unicode {f817}^4-n^2 unicode {f817}^4+a unicode {f817}^4-n unicode {f817}^4-a^2 unicode {f817}^2+2 n^2 unicode {f817}^2+a unicode {f817}^2+2 n unicode {f817}^2-n^2-nright ) unicode {f818}(unicode {f817})+left (unicode {f817}^4-unicode {f817}^2right ) unicode {f818}''(unicode {f817})=0,unicode {f818}(2)=c\_1,unicode {f818}'(2)=c\_2right }right )(x)right }right }}$$

Maple: cpu = 0.172 (sec), leaf count = 109 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{C}(0,-n-\frac{1}{2},-2,-\frac{a^2}{4}+\frac{n^2}{4}-\frac{a}{4}+\frac{n}{4},-\frac{n^2}{4}-\frac{n}{4}+\frac{3}{4}+\frac{a^2}{4}-\frac{a}{4},x^2)x^{-n}+\mathit{\_}\mathit{C}\mathit{2}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{C}(0,n+\frac{1}{2},-2,-\frac{a^2}{4}+\frac{n^2}{4}-\frac{a}{4}+\frac{n}{4},-\frac{n^2}{4}-\frac{n}{4}+\frac{3}{4}+\frac{a^2}{4}-\frac{a}{4},x^2)x^{n+1}\}$$