3.272   ODE No. 272

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

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

Mathematica: cpu = 0.044506 (sec), leaf count = 42 $$\text{Solve}[\log \left(\frac{y(x)}{x}\right)+\frac{2{\tan }^{-1}\left(\frac{\frac{2y(x)}{x}-1}{\sqrt{3}}\right)}{\sqrt{3}}=c_1-\log (x),y(x)]$$

Maple: cpu = 0.109 (sec), leaf count = 43 $$\{y\left(x\right)={\mathrm{e}}^{\frac{2\sqrt{3}}{3}\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\sqrt{3}x{\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{1}}+3\tan \left(\mathit{\_}\mathit{Z}\right)x{\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{1}}+2\sqrt{3}{\mathrm{e}}^{2/3\sqrt{3}\mathit{\_}\mathit{Z}})-\mathit{\_}\mathit{C}\mathit{1}}\}$$