8.67   ODE No. 1657

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+{\left(y\left(x\right)\right)}^3\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-y\left(x\right)\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)\sqrt{{\left(y\left(x\right)\right)}^4+4\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}=0}}$$

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

Mathematica: cpu = 0.152019 (sec), leaf count = 33 $$\left\{\{y(x)\to \sqrt{2}{e}^{c_1}\tan \left(2\sqrt{2}{e}^{3c_1}(c_2+x)\right)\}\right\}$$

Maple: cpu = 0.187 (sec), leaf count = 47 $$\{y\left(x\right)=\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}\tan (\mathit{\_}\mathit{C}\mathit{2}{\left({\mathit{\_}\mathit{C}\mathit{1}}^{-2}\right)}^{\frac{3}{2}}+x{\left({\mathit{\_}\mathit{C}\mathit{1}}^{-2}\right)}^{\frac{3}{2}}),y\left(x\right)=\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}\tanh (\mathit{\_}\mathit{C}\mathit{2}{\left({\mathit{\_}\mathit{C}\mathit{1}}^{-2}\right)}^{\frac{3}{2}}+x{\left({\mathit{\_}\mathit{C}\mathit{1}}^{-2}\right)}^{\frac{3}{2}})\}$$