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Solve the given nonlinear plane autonomous system by changing to polar coordinates. x' = y + x(x² + y2) y' = -x + y(x² + y²), X(0) = (8, 0) (r(t), 0(t)) = (solution of initial value problem) Describe the geometric behavior of the solution that satisfies the given initial condition. O The solution satisfies r → 0 as t→ 1/128 and is a spiral. O The solution satisfies r→ 0 as t→ ∞ and is a spiral. O The solution satisfies r → 0 as t→ 1/128 and is not a spiral. O The solution satisfies → ∞ as t→ 1/128 and is not a spiral. The solution satisfies → ∞ as t→ 1/128 and is a spiral.

Solve the given nonlinear plane autonomous system by changing to polar coordinates. x' = y + x(x² + y2) y' = -x + y(x² + y²), X(0) = (8, 0) (r(t), 0(t)) = (solution of initial value problem) Describe the geometric behavior of the solution that satisfies the given initial condition. O The solution satisfies r → 0 as t→ 1/128 and is a spiral. O The solution satisfies r→ 0 as t→ ∞ and is a spiral. O The solution satisfies r → 0 as t→ 1/128 and is not a spiral. O The solution satisfies → ∞ as t→ 1/128 and is not a spiral. The solution satisfies → ∞ as t→ 1/128 and is a spiral.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve the given nonlinear plane autonomous system by changing to polar coordinates. x' = y + x(x² + y2) y' = -x + y(x² + y²), X(0) = (8, 0) (r(t), 0(t)) = (solution of initial value problem) Describe the geometric behavior of the solution that satisfies the given initial condition. O The solution satisfies r → 0 as t→ 1/128 and is a spiral. O The solution satisfies r→ 0 as t→ ∞ and is a spiral. O The solution satisfies r → 0 as t→ 1/128 and is not a spiral. O The solution satisfies → ∞ as t→ 1/128 and is not a spiral. The solution satisfies → ∞ as t→ 1/128 and is a spiral.
Transcribed Image Text:Solve the given nonlinear plane autonomous system by changing to polar coordinates. x' = y + x(x² + y2) y' = -x + y(x² + y²), X(0) = (8, 0) (r(t), 0(t)) = (solution of initial value problem) Describe the geometric behavior of the solution that satisfies the given initial condition. O The solution satisfies r → 0 as t→ 1/128 and is a spiral. O The solution satisfies r→ 0 as t→ ∞ and is a spiral. O The solution satisfies r → 0 as t→ 1/128 and is not a spiral. O The solution satisfies → ∞ as t→ 1/128 and is not a spiral. The solution satisfies → ∞ as t→ 1/128 and is a spiral.
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