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 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? Tags differential equations, states, steady, steady states Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post jonatron5 Economics 2 April 13th, 2017 11:12 AM Leen Number Theory 5 April 11th, 2014 10:51 AM betelgeuse91 New Users 2 May 15th, 2011 10:31 AM becko Computer Science 8 July 16th, 2010 05:58 AM BrainMan Advanced Statistics 0 March 16th, 2009 04:41 PM

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