Solved: In 2326, solve the given nonlinear plane autonomous system by changing to polar
Chapter 11, Problem 25(choose chapter or problem)
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).
\(x^{\prime}=-y+x\left(1-x^{2}-y^{2}\right)\)
\(y^{\prime}=x+y\left(1-x^{2}-y^{2}\right)\), X(0) = (1, 0); X(0)=(2, 0)
[Hint: The resulting differential equation for r is a Bernoulli differential equation. See Section 2.5.]
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