Solve the given nonlinear plane autonomous system by changing to polar coordinates. x' = y - y' = -x - X(0) = (1, 0) X √

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Solve The Given Nonlinear Plane Autonomous System By Changing To Polar Coordinates X Y Y X X 0 1 0 X 1 (72.33 KiB) Viewed 43 times

Solve the given nonlinear plane autonomous system by changing to polar coordinates. x' = y - y' = -x - X(0) = (1, 0) X √x² + y² (4. (r(t), 8(t)) = (4-x² - y²) (solution of initial value problem) Describe the geometric behavior of the solution that satisfies the given initial condition. The solution approaches the origin on the ray 0 = 0 as t increases. The solution spirals toward the circle r = 2 as t increases. The solution traces the circle r = 2 in the clockwise direction as t increases. (r(t), 8(t)) = x² + y² (4- x² - y²), The solution spirals away from the origin with increasing magnitude as t increases. The solution spirals toward the origin as t increases. X(0) = (2, 0) (solution of initial value problem) Describe the geometric behavior of the solution that satisfies the given initial condition. The solution approaches the origin on the ray 0 = 0 as t increases. The solution spirals toward the circle r = 2 as t increases. The solution traces the circle r = 2 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.