Question: Show that the system x = y - x, y = -4x- y. is not a gradient system, but has a Lyapunov function of

Show that the system x = y - x, y = -4x- y. is not a gradient system, but has a Lyapunov function of the form

Show that the system x = y - x, y = -4x- y. is not a gradient system, but has a Lyapunov function of the form (3) - Ax + By, for some constants A, B R. Find A, B and sketch the phase portrait near the origin. V: R R;

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To show that the given system is not a gradient system we need to demonstrate that there is no potential function whose gradient matches the vector field of the system Lets assume there exists a poten... View full answer

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