1. The problem statement, all variables and given/known data This is the autonomous differential equation: x" - 2x' + 37x = 0 Solve the above DEQ and state whether the critical point (0,0) is stable, unstable, or semi-stable. 2. Relevant equations Solution to the above DEQ is x = c1excos6x + c2exsin6x 3. The attempt at a solution I worked out the solution using the quadratic formula and got roots 1[tex]\pm[/tex]6i. This gives you an [tex]\alpha[/tex] of 1 and a [tex]\beta[/tex] of 6, which yields the equation I put in part 2 above. From there, I read that when you get a general solution in the form x = e[tex]\alpha[/tex]t(c1cos[tex]\beta[/tex]t + c2sin[tex]\beta[/tex]t) with [tex]\alpha[/tex] < 0 and [tex]\beta[/tex] [tex]\neq[/tex]0, then you have a spiral point. My problem is I'm not sure how to classify the stability of the critical point (0,0).