3.425   ODE No. 425

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

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

Mathematica: cpu = 0.270034 (sec), leaf count = 59 $$\{\{y(x)\to -\frac{e^{c_1}(e^{c_1}-2x)}{2(e^{c_1}+2)}\},\{y(x)\to -\frac{2e^{c_1}(2e^{c_1}-x)}{2e^{c_1}+1}\}\}$$

Maple: cpu = 0.562 (sec), leaf count = 59 $$\{y\left(x\right)=\frac{(-{\mathit{\_}\mathit{C}\mathit{1}}^2+\mathit{\_}\mathit{C}\mathit{1})x}{-\mathit{\_}\mathit{C}\mathit{1}+1}-\frac{{\mathit{\_}\mathit{C}\mathit{1}}^2}{-\mathit{\_}\mathit{C}\mathit{1}+1},y\left(x\right)=x+2-2\sqrt{1+x},y\left(x\right)=x+2+2\sqrt{1+x}\}$$