8.146   ODE No. 1736

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

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

Mathematica: cpu = 8.595591 (sec), leaf count = 285 $$\{\{y(x)\to \text{InverseFunction}[-\frac{2i{\mathrm{\#}\text{1}}^{3/2}\sqrt{(-1{)}^{5/6}(\frac{\sqrt[3]{-c_1}}{\mathrm{\#}\text{1}}-1)}\sqrt{\frac{(-c_1){}^{2/3}}{{\mathrm{\#}\text{1}}^2}+\frac{\sqrt[3]{-c_1}}{\mathrm{\#}\text{1}}+1}F({\sin }^{-1}\left(\frac{\sqrt{-\frac{i\sqrt[3]{-c_1}}{\mathrm{\#}\text{1}}-(-1{)}^{5/6}}}{\sqrt[4]{3}}\right)|\sqrt[3]{-1})}{\sqrt[4]{3}\sqrt[3]{-c_1}\sqrt{{\mathrm{\#}\text{1}}^3+c_1}}\mathrm{\&}][c_2+x]\},\{y(x)\to \text{InverseFunction}\left[\frac{2i{\mathrm{\#}\text{1}}^{3/2}\sqrt{(-1{)}^{5/6}(\frac{\sqrt[3]{-c_1}}{\mathrm{\#}\text{1}}-1)}\sqrt{\frac{(-c_1){}^{2/3}}{{\mathrm{\#}\text{1}}^2}+\frac{\sqrt[3]{-c_1}}{\mathrm{\#}\text{1}}+1}F({\sin }^{-1}\left(\frac{\sqrt{-\frac{i\sqrt[3]{-c_1}}{\mathrm{\#}\text{1}}-(-1{)}^{5/6}}}{\sqrt[4]{3}}\right)|\sqrt[3]{-1})}{\sqrt[4]{3}\sqrt[3]{-c_1}\sqrt{{\mathrm{\#}\text{1}}^3+c_1}}\mathrm{\&}\right][c_2+x]\}\}$$

Maple: cpu = 1.654 (sec), leaf count = 49 $$\{{\int }^{y\left(x\right)}\frac{1}{\sqrt{{\mathit{\_}\mathit{a}}^4+\mathit{\_}\mathit{a}\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\frac{1}{\sqrt{{\mathit{\_}\mathit{a}}^4+\mathit{\_}\mathit{a}\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$