given plane nomous system by changing to polar cool X (36 - x² - y²) x² + y² -√x² + y² (36-x² - y²), (solution of initial value problem) (r(t), 8(t)) = | niine x' = y - y' = -x X(0) = (1, 0) -t
given plane nomous system by changing to polar cool X (36 - x² - y²) x² + y² -√x² + y² (36-x² - y²), (solution of initial value problem) (r(t), 8(t)) = | niine x' = y - y' = -x X(0) = (1, 0) -t
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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Transcribed Image Text:Solve the given nonlinear plane autonomous system by changing to polar coordinates.
X
x' = y -
(36 - x² - y²)
x² + y²
y
y' = -x -
√ x ²2² +²2²
X(0) = (1, 0)
(r(t), 0(t)) = -t
(solution of initial value problem)
X
(36 - x² - y²),
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