4.122   ODE No. 1122

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

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

Mathematica: cpu = 10.079280 (sec), leaf count = 56 $$\left\{\{y(x)\to c_2{e}^{\frac{x^2}{2}}{\int }_1^x\frac{e^{-\frac{1}{2}K[1{]}^2-K[1]}}{K[1{]}^2}dK[1]+c_1{e}^{\frac{x^2}{2}}\}\right\}$$

Maple: cpu = 0.125 (sec), leaf count = 34 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\frac{x^2}{2}}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\frac{x^2}{2}}\int \frac{1}{x^2}{\mathrm{e}}^{-\frac{x(x+2)}{2}}\mathrm{d}x\}$$