3.407   ODE No. 407

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

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

Mathematica: cpu = 0.020503 (sec), leaf count = 51 $$\{\{y(x)\to \frac{1}{4}(-4c_1\sqrt{x}+c_1^2+4x)\},\{y(x)\to \frac{1}{4}(4c_1\sqrt{x}+c_1^2+4x)\}\}$$

Maple: cpu = 0.499 (sec), leaf count = 39 $$\{y\left(x\right)=0,y\left(x\right)=\frac{1}{x}{(-x+\sqrt{\mathit{\_}\mathit{C}\mathit{1}x})}^2,y\left(x\right)=\frac{1}{x}{(x+\sqrt{\mathit{\_}\mathit{C}\mathit{1}x})}^2\}$$