Question

Please Help!!!
How do eigenvalues determine expected behavior of the solution to an Ordinary differential Equation?

Answer 1

the eigenvalues of a linear system correspond to the roots of the characteristic equation of the equivalent n'th order single DE ...... ie one with constant coefficients.

a specific problem might be insightful.

hope that helped... :p

Answer 2

Thank you :)
We were just given examples of eigenvalues and asked if we can determine the behavior of the solution of the ODE from the eigenvalues
e.g
a) 0.61
-1.61
-1

b) 0.61
0.53
0.42

c) -0.34
-0.25
-0.28

I hope this makes sense :)

Answer 3

thank you robert, it might do !!!!

"if" you are trying to classify fixed points in DE's, then b) is unstable and c) is stable. the e values tell you that. and a) looks like a saddle.

if that is not the language you were expecting, i have missed the point....and mea culpa😚

Answer 4

Haha thank you I think I get it!
Is it because a) is a mix of +ve and -ve
b) is all positive
and c) is all negative

Answer 5

indeedy!!

Answer 6

Thank you so much for helping me! :)