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Lets say I have:

$\ y''(t) + 3y'(t) + 4y(t)$ = 0

with characteristic equation

$\ x^2 + 3x + 4$ = 0

What implications about the plot of the solution to the diffeq can be drawn from the characteristic equation? I know that the coefficient to $\ y'(t)$ is the damping term and we can determine if it is over/critically damped by comparing it to a function of the coefficient to the $\ y(t)$ term (don't remember it off the top of my head). What else am I missing?

UPDATE: I know how to solve the diffeq. My question is what implications about the solution can be made from the characteristic equation BEFORE solving all the way. I mean in terms of damping, convergence, resonance, etc.

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    Hard to give an explicit answer - but you can write your system easily as $\cdot{y}=...,\cdot{x} = y$ and then discuss its eigenvalues (equation for such eigenvalues will be the same as yours).2011-10-10

2 Answers 2