11.10   ODE No. 1922

$$\boxed{{\displaystyle \{\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)=-y\left(t\right)+\{\begin{array}{ll}x\left(t\right)({\left(x\left(t\right)\right)}^2+{\left(y\left(t\right)\right)}^2-1)\sin \left({({\left(x\left(t\right)\right)}^2+{\left(y\left(t\right)\right)}^2)}^{-1}\right)& {\left(x\left(t\right)\right)}^2+{\left(y\left(t\right)\right)}^2\ne 1\\ 0& \text{otherwise}\end{array},\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)=x\left(t\right)+\{\begin{array}{ll}y\left(t\right)({\left(x\left(t\right)\right)}^2+{\left(y\left(t\right)\right)}^2-1)\sin \left({({\left(x\left(t\right)\right)}^2+{\left(y\left(t\right)\right)}^2)}^{-1}\right)& {\left(x\left(t\right)\right)}^2+{\left(y\left(t\right)\right)}^2\ne 1\\ 0& \text{otherwise}\end{array}\}}}$$

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

Mathematica: cpu = 11.112911 (sec), leaf count = 106 $$\text{DSolve}[\{x^{\prime }(t)=\left(\begin{array}{cc}\{& \begin{array}{cc}\sin \left(\frac{1}{x(t{)}^2+y(t{)}^2}\right)x(t)(x(t{)}^2+y(t{)}^2-1)& x(t{)}^2+y(t{)}^2\ne 1\\ 0& \text{True}\end{array}\end{array}\right)-y(t),y^{\prime }(t)=\left(\begin{array}{cc}\{& \begin{array}{cc}\sin \left(\frac{1}{x(t{)}^2+y(t{)}^2}\right)y(t)(x(t{)}^2+y(t{)}^2-1)& x(t{)}^2+y(t{)}^2\ne 1\\ 0& \text{True}\end{array}\end{array}\right)+x(t)\},\{x(t),y(t)\},t]$$

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