4.242   ODE No. 1242

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

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

Mathematica: cpu = 0.074509 (sec), leaf count = 68 $$\left\{\{y(x)\to c_1{e}^{-x}(x+1{)}^2-c_2{e}^{-x-2}(x^2(-\text{Ei}(2(x+1)))-2x\text{Ei}(2(x+1))-\text{Ei}(2(x+1))+2e^{2x+2})\}\right\}$$

Maple: cpu = 0.063 (sec), leaf count = 42 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-x}{(1+x)}^2+\mathit{\_}\mathit{C}\mathit{2}({\mathrm{e}}^{-2-x}{(1+x)}^2\mathit{E}\mathit{i}(1,-2x-2)+2{\mathrm{e}}^x)\}$$