4.262   ODE No. 1262

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

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

Mathematica: cpu = 38.898939 (sec), leaf count = 87 $$\left\{\{y(x)\to c_2{e}^{-x}{\int }_1^x(K[1]+1{)}^{\frac{K[1]}{K[1]+1}+\frac{1}{K[1]+1}}\exp (-\frac{K[1{]}^2}{K[1]+1}-\frac{K[1]}{K[1]+1}+2K[1]-\frac{1}{K[1]+1})dK[1]+c_1{e}^{-x}\}\right\}$$

Maple: cpu = 0.171 (sec), leaf count = 55 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-x}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{D}(4,4,-8,12,\frac{x}{x+2})(1+x)+\mathit{\_}\mathit{C}\mathit{2}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{D}(-4,4,-8,12,\frac{x}{x+2})(1+x){\mathrm{e}}^{\frac{x-1}{2x+2}}\}$$