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Given some differential equations, ie. "a", or "b":

a. $$Y'''+Y''+2Y'+KY=0$$

b. $$Y'''+KY''+3KY'+2Y=0$$

How do I get the $K$ values that make the solution stable?

I know that for "a", it should be $0 < K <2$ and that for "b" the solution is $K>(\frac2{3})^{1/2}$ but I didn't figure that out by myself.

Joao
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Luis
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1 Answers1

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Well, I came with an answer myself.

The most efficient way to get a stable solution, is via the Routh Hurwitz stability criterion. http://en.wikipedia.org/wiki/Routh%E2%80%93Hurwitz_stability_criterion

For a third-order polynomial

$P(s) = a_3s^3 + a_2s^2 + a_1s + a_0 = 0$

all the coefficients must satisfy:

$ a_n > 0 $

$ a_2a_1 > a_3a_0 $

Luis
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