Solve the given nonlinear plane autonomous system by changing to polar coordinates x y x...

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Solve the given nonlinear plane autonomous system by changing to polar coordinates x y x x y y xy x y r t 8 t x 0 5 0 solution of initial value problem X Describe the geometric behavior of the solution that satisfies the given initial condition s The solution spirals away from the origin with increasing magnitude as t increases O O The solution traces the circle r 5 in the clockwise direction as t increases O The solution spirals toward the circle r 1 as t increases The solution approaches the origin on the ray 0 0 as t increases The solution spirals toward the origin as t increases

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Solve the given nonlinear plane autonomous system by changing to polar coordinates x y x x y y xy x y r t 8 t x 0 5 0 solution of initial value problem X Describe the geometric behavior of the solution that satisfies the given initial condition s The solution spirals away from the origin with increasing magnitude as t increases O O The solution traces the circle r 5 in the clockwise direction as t increases O The solution spirals toward the circle r 1 as t increases The solution approaches the origin on the ray 0 0 as t increases The solution spirals toward the origin as t increases