3.716   ODE No. 716

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{3x^4+3x^3+\sqrt{9x^4-4{\left(y\left(x\right)\right)}^3}}{(1+x){\left(y\left(x\right)\right)}^2}=0}}$$

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

Mathematica: cpu = 5.769733 (sec), leaf count = 133 $$\{\{y(x)\to {(-\frac{3}{2})}^{2/3}\sqrt[3]{8c_1\log (x+1)-4c_1^2+x^4-4{\log }^2(x+1)}\},\{y(x)\to {\left(\frac{3}{2}\right)}^{2/3}\sqrt[3]{8c_1\log (x+1)-4c_1^2+x^4-4{\log }^2(x+1)}\},\{y(x)\to -\sqrt[3]{-1}{\left(\frac{3}{2}\right)}^{2/3}\sqrt[3]{8c_1\log (x+1)-4c_1^2+x^4-4{\log }^2(x+1)}\}\}$$

Maple: cpu = 0.249 (sec), leaf count = 37 $$\{{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}{\mathit{\_}\mathit{a}}^2\frac{1}{\sqrt{9x^4-4{\mathit{\_}\mathit{a}}^3}}\mathrm{d}\mathit{\_}\mathit{a}-\ln (1+x)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$