3.652   ODE No. 652

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

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

Mathematica: cpu = 1.924244 (sec), leaf count = 101 $$\{\{y(x)\to -\frac{\sqrt{4096a^{5}x-256a^4{x}^4+32a^2{e}^{c_1}{x}^2-e^{2c_1}}}{32a^2}\},\{y(x)\to \frac{\sqrt{4096a^{5}x-256a^4{x}^4+32a^2{e}^{c_1}{x}^2-e^{2c_1}}}{32a^2}\}\}$$

Maple: cpu = 0.124 (sec), leaf count = 27 $$\{-\sqrt{-{\left(y\left(x\right)\right)}^2+4ax}-\frac{x^2}{2}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$