7. [-/1 Points] DETAILS Solve the given nonlinear plane autonomous system by changing to polar coordinates. x' = Y - y'

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7 1 Points Details Solve The Given Nonlinear Plane Autonomous System By Changing To Polar Coordinates X Y Y 1 (80.02 KiB) Viewed 38 times

7. [-/1 Points] DETAILS Solve the given nonlinear plane autonomous system by changing to polar coordinates. x' = Y - y' = -x - X(0)= (1, 0) ZILLDIFFEQ9 10.1.026. X x² + y2 y (r(t), 8(t)) x² (16-x² - y²) +y² (16 - x² - y²), (r(t), 8(t)) Describe the geometric behavior of the solution that satisfies the given initial condition. O The solution approaches the origin on the ray = 0 as t increases. O The solution spirals toward the circler - 4 as t increases. The solution traces the circle r 4 in the clockwise direction as t increases. O The solution spirals away from the origin with increasing magnitude as t increases. O The solution spirals toward the origin as t increases. X(0)-(4,0) (solution of initial value problem) (solution of initial value problem) Describe the geometric behavior of the solution that satisfies the given initial condition. O The solution approaches the origin on the ray 0 - 0 as t increases. O The solution spirals toward the circler 4 as t increases. O The solution traces the circler 4 in the clockwise direction as t increases. The solution spirals away from the origin with increasing magnitude as t increases. The solution spirals toward the origin as 't increases.