Chapter 10.1, Problem 26E

In Problems 23–26 solve the given nonlinear plane autonomous system by changing to polar coordinates. Describe the geometric behavior of the solution that satisfies the given initial condition(s).

26. $\begin{array}{l}{x}^{\prime }=y-\frac{x}{\sqrt{x^2+y^2}}(4-x^2-y^2)\hfill \\ y^{\prime }=-x-\frac{y}{\sqrt{x^2+y^2}}(4-x^2-y^2),\hfill \\ X(0)=(1,0),X(0)=(2,0)\hfill \end{array}$