4.307   ODE No. 1307

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

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

Mathematica: cpu = 0.085011 (sec), leaf count = 54 $$\left\{\{y(x)\to \frac{c_1{e}^{\frac{1}{x}}(x+1)}{x}-\frac{c_2(e^{\frac{1}{x}}x\text{Ei}(-\frac{1}{x})+e^{\frac{1}{x}}\text{Ei}(-\frac{1}{x})+x)}{x}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 38 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{x^{-1}}(1+x)}{x}+\frac{\mathit{\_}\mathit{C}\mathit{2}(-{\mathrm{e}}^{x^{-1}}(1+x)\mathit{E}\mathit{i}(1,x^{-1})+x)}{x}\}$$