11.9   ODE No. 1921

$$\boxed{{\displaystyle \{\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)=-y\left(t\right)({\left(x\left(t\right)\right)}^2+{\left(y\left(t\right)\right)}^2),\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)=\{\begin{array}{ll}{\left(x\left(t\right)\right)}^2+{\left(y\left(t\right)\right)}^2& 2x\left(t\right)\le {\left(x\left(t\right)\right)}^2+{\left(y\left(t\right)\right)}^2\\ (1/2x\left(t\right)-1/2\frac{{\left(y\left(t\right)\right)}^2}{x\left(t\right)})({\left(x\left(t\right)\right)}^2+{\left(y\left(t\right)\right)}^2)& \text{otherwise}\end{array}\}}}$$

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

Mathematica: cpu = 2.354299 (sec), leaf count = 86 $$\text{DSolve}[\{x^{\prime }(t)=-y(t)(x(t{)}^2+y(t{)}^2),y^{\prime }(t)=\left(\begin{array}{cc}\{& \begin{array}{cc}x(t{)}^2+y(t{)}^2& x(t{)}^2+y(t{)}^2\ge 2x(t)\\ (x(t{)}^2+y(t{)}^2)(\frac{x(t)}{2}-\frac{y(t{)}^2}{2x(t)})& \text{True}\end{array}\end{array}\right)\},\{x(t),y(t)\},t]$$

Maple: cpu = 0 (sec), leaf count = 0 $$\text{hanged}$$