- Solve The Given Nonlinear Plane Autonomous System By Changing To Polar Coordinates 1 (47.8 KiB) Viewed 38 times
Solve the given nonlinear plane autonomous system by changing to polar coordinates.
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Solve the given nonlinear plane autonomous system by changing to polar coordinates.
Solve the given nonlinear plane autonomous system by changing topolar coordinates.
Solve the given nonlinear plane autonomous system by changing to polar coordinates. (36x² - y²) (r(t), 8(t)) x' = y - y' = X(0) = (1, 0) = X (r(t), 8(t)) = x + (36 - x² - y²), (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 circle r = 6 as t increases. O The solution traces the circle r = 6 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) = (6, 0) (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 circle r = 6 as t increases. O The solution traces the circle r = 6 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.
Solve the given nonlinear plane autonomous system by changing to polar coordinates. (36x² - y²) (r(t), 8(t)) x' = y - y' = X(0) = (1, 0) = X (r(t), 8(t)) = x + (36 - x² - y²), (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 circle r = 6 as t increases. O The solution traces the circle r = 6 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) = (6, 0) (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 circle r = 6 as t increases. O The solution traces the circle r = 6 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.