Answer Happy

Solve the given nonlinear plane autonomous system by changing to polar coordinates. x' = y - y' = -x - X 2 V x² + (r(t), 0(t)) = X(0) = = (1, 0) (r(t), 0(t)) = y V x² + (64 - x² - y²) (64 - 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 = 8 as t increases. The solution traces the circle r = 8 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. X(0) = = (8,0) (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 = 8 as t increases. The solution traces the circle r = 8 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.