3.845   ODE No. 845

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

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

Mathematica: cpu = 4.914124 (sec), leaf count = 227 $$\{\{y(x)\to -\frac{1}{2}\sqrt[3]{-\frac{1}{2}}\sqrt[3]{72c_1{x}^4+96c_1{x}^3+288c_{1}x+144c_1^2+9x^8+24x^7+16x^6+72x^5+132x^4+144x^2}\},\{y(x)\to \frac{\sqrt[3]{72c_1{x}^4+96c_1{x}^3+288c_{1}x+144c_1^2+9x^8+24x^7+16x^6+72x^5+132x^4+144x^2}}{2\sqrt[3]{2}}\},\{y(x)\to \frac{(-1{)}^{2/3}\sqrt[3]{72c_1{x}^4+96c_1{x}^3+288c_{1}x+144c_1^2+9x^8+24x^7+16x^6+72x^5+132x^4+144x^2}}{2\sqrt[3]{2}}\}\}$$

Maple: cpu = 0.187 (sec), leaf count = 44 $$\{{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}{\mathit{\_}\mathit{a}}^2\frac{1}{\sqrt{-9x^4+4{\mathit{\_}\mathit{a}}^3}}\mathrm{d}\mathit{\_}\mathit{a}-\frac{x^4}{4}-\frac{x^3}{3}-x-\mathit{\_}\mathit{C}\mathit{1}=0\}$$