ODE No. 1922

$$\{x^{\prime }(t)=\left(\begin{array}{cc}\{& \begin{array}{cc}\sin \left(\frac{1}{x(t{)}^2+y(t{)}^2}\right)x(t)(x(t{)}^2+y(t{)}^2-1)& x(t{)}^2+y(t{)}^2\ne 1\\ 0& \text{True}\end{array}\end{array}\right)-y(t),y^{\prime }(t)=\left(\begin{array}{cc}\{& \begin{array}{cc}\sin \left(\frac{1}{x(t{)}^2+y(t{)}^2}\right)y(t)(x(t{)}^2+y(t{)}^2-1)& x(t{)}^2+y(t{)}^2\ne 1\\ 0& \text{True}\end{array}\end{array}\right)+x(t)\}$$ ✗ Mathematica : cpu = 8.57945 (sec), leaf count = 0

DSolve[{Derivative[1][x][t] == Piecewise[{{Sin[(x[t]^2 + y[t]^2)^(-1)]*x[t]*(-1 + x[t]^2 + y[t]^2), x[t]^2 + y[t]^2 != 1}}, 0] - y[t], Derivative[1][y][t] == Piecewise[{{Sin[(x[t]^2 + y[t]^2)^(-1)]*y[t]*(-1 + x[t]^2 + y[t]^2), x[t]^2 + y[t]^2 != 1}}, 0] + x[t]},{x[t], y[t]},t]
 

, could not solve

DSolve[{Derivative[1][x][t] == Piecewise[{{Sin[(x[t]^2 + y[t]^2)^(-1)]*x[t]*(-1 + x[t]^2 + y[t]^2), x[t]^2 + y[t]^2 != 1}}, 0] - y[t], Derivative[1][y][t] == Piecewise[{{Sin[(x[t]^2 + y[t]^2)^(-1)]*y[t]*(-1 + x[t]^2 + y[t]^2), x[t]^2 + y[t]^2 != 1}}, 0] + x[t]}, {x[t], y[t]}, t]

✗ Maple : cpu = 0. (sec), leaf count = 0

dsolve({diff(x(t),t) = -y(t)+piecewise(x(t)^2+y(t)^2 <> 1,x(t)*(x(t)^2+y(t)^2-1)*sin(1/(x(t)^2+y(t)^2))), diff(y(t),t) = x(t)+piecewise(x(t)^2+y(t)^2 <> 1,y(t)*(x(t)^2+y(t)^2-1)*sin(1/(x(t)^2+y(t)^2)))})
 

, exception

time expired