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I am given the following two differential equations and asked to find the equilibrium points, I've looked on Pauls online notes; however, I could not find anything that was similar to my problem, any suggestions on how to attempt it would be helpful

$$x’ = 5- 0.01 x + 0.0025 y$$

$$y’ = 10 + 0.01 x – 0.01 y$$

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1 Answer

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Well, $x'= y'=0$ when \begin{align} -0.01x &&+0.0025y &= -5, \\ 0.01x && - 0.01y &= -10. \end{align} You can see we can add equations these to obtain $-0.0075y= -15$, so $y = 2000$. This gives $0.01x = -10 + 0.01(2000) = -10 + 20 =10,$ so $x= 1000$.

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