Solve the given nonlinear plane autonomous system by changing to polar coordinates. x' = y + x(x2 + y2) y' = −x + y(x2 +

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Solve the given nonlinear plane autonomous system by changing topolar coordinates.
x' = y + x(x2 + y2)
y' = −x + y(x2 + y2), X(0)= (8, 0)
(r(t), 𝜃(t)) = ? (solution of initial value problem)
Describe the geometric behavior of the solution that satisfiesthe given initial condition.(pick one below)
The solutionsatisfies r → ∞ as t → 1/128 andis a spiral.
The solutionsatisfies r → ∞ as t → 1/128 andis not a spiral.
The solution satisfies r → 0as t → 1/128 and is a spiral.
The solution satisfies r → 0as t → ∞ and is a spiral.
The solution satisfies r → 0as t → 1/128 and is not a spiral.