3.831   ODE No. 831

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

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

Mathematica: cpu = 4.434063 (sec), leaf count = 145 $$\{\{y(x)\to -\frac{1}{12}\sqrt{576ax-72c_1{x}^4-96c_1{x}^3-288c_{1}x-144c_1^2-9x^8-24x^7-16x^6-72x^5-96x^4-144x^2}\},\{y(x)\to \frac{1}{12}\sqrt{576ax-72c_1{x}^4-96c_1{x}^3-288c_{1}x-144c_1^2-9x^8-24x^7-16x^6-72x^5-96x^4-144x^2}\}\}$$

Maple: cpu = 0.234 (sec), leaf count = 35 $$\{-\sqrt{-{\left(y\left(x\right)\right)}^2+4ax}-\frac{x^4}{4}-\frac{x^3}{3}-x-\mathit{\_}\mathit{C}\mathit{1}=0\}$$