Question

Differential Equations: Variation of Parameters.
y''+4y'+4y=t^(-2)e^(-2t)

Answer 1

Try http://tutorial.math.lamar.edu/Classes/DE/VariationofParameters.aspx

Answer 2

Start off with homogenous solution.

Answer 3

the problem i have is with \[y(t)=c _{1}e ^{-2t}+c _{2}e ^{-2t}t\]

Answer 4

im not sure where the t at the end comes from

Answer 5

The t comes from the fact that the polynomial has repeated roots.

Answer 6

is there a theorem for that?

Answer 7

If you have n repeated roots you will in general have n factors of t. So if you had:
\[(\lambda-r)^n \implies c_1e^{rt}+c_2te^{rt}+...+c_n t^n e^{rt}\]

Answer 8

This is goodish:
http://ltcconline.net/greenl/courses/204/ConstantCoeff/repeatedRoots.htm

Answer 9

oh i see, thank you very much

Answer 10

No problem :)