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

Question

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

anonymous · Answer

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

anonymous · Answer

Start off with homogenous solution.

anonymous · Answer

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

anonymous · Answer

im not sure where the t at the end comes from

anonymous · Answer

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

anonymous · Answer

is there a theorem for that?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

oh i see, thank you very much

anonymous · Answer

No problem :)