\[ \left \{x'(t)=\left (\begin {array}{cc} \{ & \begin {array}{cc} \sin \left (\frac {1}{x(t)^2+y(t)^2}\right ) x(t) \left (x(t)^2+y(t)^2-1\right ) & x(t)^2+y(t)^2\neq 1 \\ 0 & \text {True} \\\end {array} \\\end {array}\right )-y(t),y'(t)=\left (\begin {array}{cc} \{ & \begin {array}{cc} \sin \left (\frac {1}{x(t)^2+y(t)^2}\right ) y(t) \left (x(t)^2+y(t)^2-1\right ) & x(t)^2+y(t)^2\neq 1 \\ 0 & \text {True} \\\end {array} \\\end {array}\right )+x(t)\right \} \] ✗ Mathematica : cpu = 12.0507 (sec), leaf count = 0 , 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 , exception
time expired