4.194   ODE No. 1194

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

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

Mathematica: cpu = 0.049506 (sec), leaf count = 65 $$\left\{\{y(x)\to c_1{e}^{-x}(x-3)x-\frac{c_2{e}^{-x}(x^3(-\text{Ei}(x))+3x^2\text{Ei}(x)+e^x{x}^2-2e^{x}x-e^x)}{6x}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 44 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x{\mathrm{e}}^{-x}(x-3)+\frac{\mathit{\_}\mathit{C}\mathit{2}(x^2{\mathrm{e}}^{-x}(x-3)\mathit{E}\mathit{i}(1,-x)+x^2-2x-1)}{x}\}$$