4.361   ODE No. 1361

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

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

Mathematica: cpu = 0.471560 (sec), leaf count = 38 $$\left\{\{y(x)\to c_1{x}^{-a}+c_2(-2a{x}^2+2a-x^2+3)x^{a+1}\}\right\}$$

Maple: cpu = 0.015 (sec), leaf count = 33 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{-a}+\mathit{\_}\mathit{C}\mathit{2}{x}^{a+1}(2a{x}^2+x^2-2a-3)\}$$