2.720   ODE No. 720

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

$$y^{\prime }(x)=\frac{x^3(\sqrt{9x^4-4y(x{)}^3}+3x+3)}{(x+1)y(x{)}^2}$$ ✓ Mathematica : cpu = 4.36525 (sec), leaf count = 314

$$\{\{y(x)\to \sqrt[3]{6c_1{x}^3-9c_1{x}^2+18c_{1}x-18c_1\log (x+1)-9c_1^2-x^6+3x^5-6x^4+9x^3+6x^3\log (x+1)-9x^2-9x^2\log (x+1)-9{\log }^2(x+1)+18x\log (x+1)}\},\{y(x)\to -\sqrt[3]{-1}\sqrt[3]{6c_1{x}^3-9c_1{x}^2+18c_{1}x-18c_1\log (x+1)-9c_1^2-x^6+3x^5-6x^4+9x^3+6x^3\log (x+1)-9x^2-9x^2\log (x+1)-9{\log }^2(x+1)+18x\log (x+1)}\},\{y(x)\to (-1{)}^{2/3}\sqrt[3]{6c_1{x}^3-9c_1{x}^2+18c_{1}x-18c_1\log (x+1)-9c_1^2-x^6+3x^5-6x^4+9x^3+6x^3\log (x+1)-9x^2-9x^2\log (x+1)-9{\log }^2(x+1)+18x\log (x+1)}\}\}$$

✓ Maple : cpu = 0.242 (sec), leaf count = 48

$$\{{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}{\mathit{\_}\mathit{a}}^2\frac{1}{\sqrt{9x^4-4{\mathit{\_}\mathit{a}}^3}}\mathrm{d}\mathit{\_}\mathit{a}-\frac{x^3}{3}+\frac{x^2}{2}-x+\ln (1+x)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$