Differential Equations Ordinary and Partial Differential Equations Math Forum

 April 4th, 2019, 10:27 AM #1 Newbie   Joined: Mar 2019 From: USA Posts: 4 Thanks: 0 Steady States For an example problem to solve in an engineering class I was given the following systems and told to find the steady states of each and the eigenvalues for each steady state. 1) $\displaystyle dx/dt = x(1-2y-x)$ $\displaystyle dy/dt = y-x$ 2) $\displaystyle x' = x(10-x-y)$ $\displaystyle y' = y(30-2x-y)$ I know that for steady states I need to solve for when the derivatives are both equal to zero. For both systems I know that x=y=0 is a trivial solution. I found another solution to be x=y=1/3 for System #1 and x=20, y=-10 for System #2. My problem is, I remember how to find eigenvalues of matrices from Lin. Alg. but I'm not sure how to get these equations into a form where I can solve for the eigenvalues. How would I go about finding the eigenvalues for these systems?

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