Solve the given nonlinear plane autonomous system by changing to polar coordinates. x¹ = y + x(x² + y²) y' = -x + y(x² +

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Solve The Given Nonlinear Plane Autonomous System By Changing To Polar Coordinates X Y X X Y Y X Y X 1 (224.63 KiB) Viewed 23 times

Solve the given nonlinear plane autonomous system by changing to polar coordinates. x¹ = y + x(x² + y²) y' = -x + y(x² + y²), X(0) = (2, 0) (r(t), 0(t)) = (solution of initial value problem) Describe the geometric behavior of the solution that satisfies the given initial condition. The solution satisfies r→ 0 as t→ 1/8 and is a spiral. The solution satisfies r → ∞ as t→ 1/8 and is a spiral. The solution satisfies r→ 0 as t→ 1/8 and is not a spiral. The solution satisfies → ∞ as t → 1/8 and is not a spiral. The solution satisfies r→ 0 as t→ ∞ and is a spiral.