By using the Liapunov function V(x, y, z) = x² + y? + z?, show that the origin of the following system is asymptotically stable. (* = -y-xy² + z² – x3 y = x+z-y 2 = -xz - x²z - yz? - z5

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A: Actually given hints is the particular solution, although i deduce this by undetermined coefficients…

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A: According to guidelines we have to solve only one question.

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A: Using matrix method

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A: see my solution below

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A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: If L(x, y) = ax + by² is a Lyapunov function at the origin for the system * = y + x³, y = -x + y³, a…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…