8.163   ODE No. 1753

$$\boxed{{\displaystyle 12\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)y\left(x\right)-15{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+8{\left(y\left(x\right)\right)}^3=0}}$$

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

Mathematica: cpu = 0.321041 (sec), leaf count = 43 $$\left\{\{y(x)\to \frac{2304c_1^2}{(3c_1^2{x}^2+6c_2{c}_1^{2}x+3c_2^2{c}_1^2+128){}^2}\}\right\}$$

Maple: cpu = 1.575 (sec), leaf count = 147 $$\{-12\frac{y\left(x\right)(8\sqrt{y\left(x\right)}-\mathit{\_}\mathit{C}\mathit{1})\sqrt{8y\left(x\right)-\mathit{\_}\mathit{C}\mathit{1}\sqrt{y\left(x\right)}}}{\sqrt{-24{\left(y\left(x\right)\right)}^3+3\mathit{\_}\mathit{C}\mathit{1}{\left(y\left(x\right)\right)}^{5/2}}\mathit{\_}\mathit{C}\mathit{1}\sqrt{\sqrt{y\left(x\right)}(8\sqrt{y\left(x\right)}-\mathit{\_}\mathit{C}\mathit{1})}}-x-\mathit{\_}\mathit{C}\mathit{2}=0,12\frac{y\left(x\right)(8\sqrt{y\left(x\right)}-\mathit{\_}\mathit{C}\mathit{1})\sqrt{8y\left(x\right)-\mathit{\_}\mathit{C}\mathit{1}\sqrt{y\left(x\right)}}}{\sqrt{-24{\left(y\left(x\right)\right)}^3+3\mathit{\_}\mathit{C}\mathit{1}{\left(y\left(x\right)\right)}^{5/2}}\mathit{\_}\mathit{C}\mathit{1}\sqrt{\sqrt{y\left(x\right)}(8\sqrt{y\left(x\right)}-\mathit{\_}\mathit{C}\mathit{1})}}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$