# Stability properties of zero solution to a nonlinear system of differential equations.

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Use the function V(x,y) = x^2 + y^2 to analyze the stability properties of the zero solution of the nonlinear system

x' = x + 2xy^2

y' = - 2x^2y + y

More specifically, what stability conclution(s) can be drawn? ( Justify your answer)

Please I want a detailed and clear solution. Thanks.

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#### Solution Summary

The stability properties of zero solution to a nonlinear system of differential equations are investigated.

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