3.749   ODE No. 749

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

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

Mathematica: cpu = 0.106013 (sec), leaf count = 126 $$\{\{y(x)\to -\frac{\sqrt{x^2{e}^{4c_1+2x^2}-e^{4c_1+2x^2}+x^2+1}}{\sqrt{e^{4c_1+2x^2}+1}}\},\{y(x)\to \frac{\sqrt{x^2{e}^{4c_1+2x^2}-e^{4c_1+2x^2}+x^2+1}}{\sqrt{e^{4c_1+2x^2}+1}}\}\}$$

Maple: cpu = 0.109 (sec), leaf count = 192 $$\{y\left(x\right)=1\sqrt{(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{x^2(x^2-2)}{2}}+{\mathrm{e}}^{-\frac{x^2(x^2+2)}{2}})((x^2+1){\mathrm{e}}^{-\frac{x^2(x^2+2)}{2}}+\mathit{\_}\mathit{C}\mathit{1}(x^2-1){\mathrm{e}}^{-\frac{x^2(x^2-2)}{2}})}{(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{x^2(x^2-2)}{2}}+{\mathrm{e}}^{-\frac{x^2(x^2+2)}{2}})}^{-1},y\left(x\right)=-1\sqrt{(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{x^2(x^2-2)}{2}}+{\mathrm{e}}^{-\frac{x^2(x^2+2)}{2}})((x^2+1){\mathrm{e}}^{-\frac{x^2(x^2+2)}{2}}+\mathit{\_}\mathit{C}\mathit{1}(x^2-1){\mathrm{e}}^{-\frac{x^2(x^2-2)}{2}})}{(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{x^2(x^2-2)}{2}}+{\mathrm{e}}^{-\frac{x^2(x^2+2)}{2}})}^{-1}\}$$