2.62   ODE No. 62

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

$$y^{\prime }(x)-\frac{y(x)-x^2\sqrt{x^2-y(x{)}^2}}{xy(x)\sqrt{x^2-y(x{)}^2}+x}=0$$ ✓ Mathematica : cpu = 3.75953 (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 = 0.406 (sec), leaf count = 34

$$\{\frac{{\left(y\left(x\right)\right)}^2}{2}+\arctan \left(y\left(x\right)\frac{1}{\sqrt{x^2-{\left(y\left(x\right)\right)}^2}}\right)+\frac{x^2}{2}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$