4.57   ODE No. 1057

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

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

Mathematica: cpu = 0.879612 (sec), leaf count = 55 $$\left\{\{y(x)\to c_2{e}^{\frac{x^3}{3}+x}{\int }_1^x{e}^{-\frac{1}{3}K[1{]}^3-2K[1]}dK[1]+c_1{e}^{\frac{x^3}{3}+x}\}\right\}$$

Maple: cpu = 0.110 (sec), leaf count = 50 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{T}(0,-3,2\sqrt[3]{3},\frac{3^{\frac{2}{3}}x}{3}){\mathrm{e}}^{-x}+\mathit{\_}\mathit{C}\mathit{2}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{T}(0,3,2\sqrt[3]{3},-\frac{3^{\frac{2}{3}}x}{3}){\mathrm{e}}^{\frac{x(x^2+3)}{3}}\}$$