Answer Happy

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.