8.124   ODE No. 1714

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

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

Mathematica: cpu = 0.060508 (sec), leaf count = 25 $$\left\{\{y(x)\to \frac{c_2{e}^x}{\sqrt{1-2e^{c_1+x}}}\}\right\}$$

Maple: cpu = 1.513 (sec), leaf count = 67 $$\{y\left(x\right)=-\frac{\sqrt{2}}{2\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^x-2\mathit{\_}\mathit{C}\mathit{2}}\sqrt{(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^x-\mathit{\_}\mathit{C}\mathit{2}){\mathrm{e}}^{2x}},y\left(x\right)=\frac{\sqrt{2}}{2\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^x-2\mathit{\_}\mathit{C}\mathit{2}}\sqrt{(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^x-\mathit{\_}\mathit{C}\mathit{2}){\mathrm{e}}^{2x}}\}$$