2.1730   ODE No. 1730

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

$$2y(x)y^{″}(x)-y^{\prime }(x{)}^2-8y(x{)}^3=0$$ ✓ Mathematica : cpu = 0.466281 (sec), leaf count = 127

$$\{\{y(x)\to -\frac{1}{2}i\sqrt{c_1}\text{ns}(\frac{1}{2}(-(-1{)}^{3/4}\sqrt{2}\sqrt[4]{c_1}x-(-1{)}^{3/4}\sqrt{2}\sqrt[4]{c_1}{c}_2)|-1){}^2\},\{y(x)\to -\frac{1}{2}i\sqrt{c_1}\text{ns}(\frac{1}{2}((-1{)}^{3/4}\sqrt{2}\sqrt[4]{c_1}x+(-1{)}^{3/4}\sqrt{2}\sqrt[4]{c_1}{c}_2)|-1){}^2\}\}$$

✓ Maple : cpu = 0.331 (sec), leaf count = 53

$$\{{\int }^{y\left(x\right)}\frac{1}{\sqrt{4{\mathit{\_}\mathit{a}}^3+\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{a}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\frac{1}{\sqrt{4{\mathit{\_}\mathit{a}}^3+\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{a}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$