3.241   ODE No. 241

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

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

Mathematica: cpu = 0.009001 (sec), leaf count = 41 $$\{\{y(x)\to -\sqrt{c_{1}x-a{x}^2}\},\{y(x)\to \sqrt{c_{1}x-a{x}^2}\}\}$$

Maple: cpu = 0.015 (sec), leaf count = 33 $$\{y\left(x\right)=\sqrt{-a{x}^2+\mathit{\_}\mathit{C}\mathit{1}x},y\left(x\right)=-\sqrt{-a{x}^2+\mathit{\_}\mathit{C}\mathit{1}x}\}$$