3.62   ODE No. 62

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

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

Mathematica: cpu = 3.807984 (sec), leaf count = 40 $$\text{Solve}[{\tan }^{-1}\left(\frac{y(x)}{\sqrt{x^2-y(x{)}^2}}\right)+\frac{x^2}{2}+\frac{y(x{)}^2}{2}=c_1,y(x)]$$

Maple: cpu = 0.297 (sec), leaf count = 34 $$\{\frac{{\left(y\left(x\right)\right)}^2}{2}+\arctan \left(y\left(x\right)\frac{1}{\sqrt{x^2-{\left(y\left(x\right)\right)}^2}}\right)+\frac{x^2}{2}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$

Sage: cpu = 0 (sec), leaf count = 0 $$\text{Maxima was unable to solve this ODE}$$