2.1921   ODE No. 1921

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

$$\{x^{\prime }(t)=-y(t)(x(t{)}^2+y(t{)}^2),y^{\prime }(t)=\left(\begin{array}{cc}\{& \begin{array}{cc}x(t{)}^2+y(t{)}^2& x(t{)}^2+y(t{)}^2\ge 2x(t)\\ (x(t{)}^2+y(t{)}^2)(\frac{x(t)}{2}-\frac{y(t{)}^2}{2x(t)})& \text{True}\end{array}\end{array}\right)\}$$ ✗ Mathematica : cpu = 2.6456 (sec), leaf count = 0 , could not solve

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

✗ Maple : cpu = 0. (sec), leaf count = 0 , could not solve

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