3.540   ODE No. 540

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

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

Mathematica: cpu = 0.019502 (sec), leaf count = 69 $$\{\{y(x)\to c_1+\frac{x}{2}\},\{y(x)\to \frac{(3c_1-2i{x}^{3/2}){}^{2/3}}{2^{2/3}}\},\{y(x)\to \frac{(3c_1+2i{x}^{3/2}){}^{2/3}}{2^{2/3}}\}\}$$

Maple: cpu = 0.047 (sec), leaf count = 109 $$\{x+\frac{\mathit{\_}\mathit{C}\mathit{1}x}{y\left(x\right)}{\left(\frac{1}{y\left(x\right)}(-\sqrt{-xy\left(x\right)}+y\left(x\right))\right)}^{-\frac{2}{3}}{\left(\frac{1}{y\left(x\right)}(-x+\sqrt{-xy\left(x\right)}+y\left(x\right))\right)}^{-\frac{2}{3}}=0,x+\frac{\mathit{\_}\mathit{C}\mathit{1}x}{y\left(x\right)}{\left(\frac{1}{y\left(x\right)}(\sqrt{-xy\left(x\right)}+y\left(x\right))\right)}^{-\frac{2}{3}}{\left(\frac{1}{y\left(x\right)}(-x-\sqrt{-xy\left(x\right)}+y\left(x\right))\right)}^{-\frac{2}{3}}=0,y\left(x\right)=\frac{x}{2}+\mathit{\_}\mathit{C}\mathit{1}\}$$