2.845   ODE No. 845

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

$$y^{\prime }(x)=\frac{x^3\sqrt{4y(x{)}^3-9x^4}+x^2\sqrt{4y(x{)}^3-9x^4}+\sqrt{4y(x{)}^3-9x^4}+3x^3}{y(x{)}^2}$$ ✓ Mathematica : cpu = 3.12535 (sec), leaf count = 266

$$\{\{y(x)\to -\frac{1}{2}\sqrt[3]{-\frac{1}{2}}\sqrt[3]{9x^8+24x^7+16x^6+72x^5+114x^4-24x^3+144x^2+72c_1{x}^4+96c_1{x}^3-72x+288c_{1}x+9+144c_1{}^2-72c_1}\},\{y(x)\to \frac{\sqrt[3]{9x^8+24x^7+16x^6+72x^5+114x^4-24x^3+144x^2+72c_1{x}^4+96c_1{x}^3-72x+288c_{1}x+9+144c_1{}^2-72c_1}}{2\sqrt[3]{2}}\},\{y(x)\to \frac{(-1{)}^{2/3}\sqrt[3]{9x^8+24x^7+16x^6+72x^5+114x^4-24x^3+144x^2+72c_1{x}^4+96c_1{x}^3-72x+288c_{1}x+9+144c_1{}^2-72c_1}}{2\sqrt[3]{2}}\}\}$$ ✓ Maple : cpu = 0.255 (sec), leaf count = 44

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