8.210   ODE No. 1800

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

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

Mathematica: cpu = 0.521066 (sec), leaf count = 84 $$\{\{y(x)\to -\frac{\sqrt{-2c_{1}x-2c_2{c}_1-1}}{\sqrt{2}\sqrt{c_{1}x+c_2{c}_1}}\},\{y(x)\to \frac{\sqrt{-2c_{1}x-2c_2{c}_1-1}}{\sqrt{2}\sqrt{c_{1}x+c_2{c}_1}}\}\}$$

Maple: cpu = 1.607 (sec), leaf count = 67 $$\{y\left(x\right)=-\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}x+2\mathit{\_}\mathit{C}\mathit{2}}\sqrt{-(2\mathit{\_}\mathit{C}\mathit{1}x+2\mathit{\_}\mathit{C}\mathit{2})(2\mathit{\_}\mathit{C}\mathit{1}x+2\mathit{\_}\mathit{C}\mathit{2}+1)},y\left(x\right)=\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}x+2\mathit{\_}\mathit{C}\mathit{2}}\sqrt{-(2\mathit{\_}\mathit{C}\mathit{1}x+2\mathit{\_}\mathit{C}\mathit{2})(2\mathit{\_}\mathit{C}\mathit{1}x+2\mathit{\_}\mathit{C}\mathit{2}+1)}\}$$