Solved: Solve the following nonlinear plane autonomous system by switching to polar
Chapter 11, Problem 11(choose chapter or problem)
Solve the following nonlinear plane autonomous system by switching to polar coordinates, and describe the geometric behavior of the solution that satisfies the given initial condition.
\(\begin{aligned}
&x^{\prime}=-y-x\left(\sqrt{x^{2}+y^{2}}\right)^{3} \\
&y^{\prime}=x-y\left(\sqrt{x^{2}+y^{2}}\right)^{3}, \quad \mathbf{X}(0)=(1,0)
\end{aligned}\)
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