Consider the system           x'= y - 4x + x2 ; y' = 4y - 2xy : (a)  Find a nonconstant function H(x , y) such that every orbit of the system satises H(x , y) = c for some constant c. (b)  The stationary points are (0; 0), (4; 0), and (2; 4). In the phase-plane sketch these stationary points plus the level set H(x; y) = c for each value of c that corresponds to a stationary point that is a saddle.

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A: Use the definition

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A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

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A: The matrix form of given system of differential equations as follows

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A: see my solution below

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A: f(1) = 4 f'(1) = -2 g(3) = 7 g'(3) = 1 f(x)g(y) = 24 + x + y

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