What is my guess for a polynomial solution with a negative highest power?

[Kyle Parrott]

Hi there, I know that when I am to guess a solution to to a polynomial for g(t) that I guess Ax^n + Bx^n-1... when the highest power of the polynomial is n but what is my guess supposed to be if the power of n is negative?

ex.
y'' + 4y' + 4y = t^-2*e^(-2t)

so far my guess is,

A*e^(-2t)(B*?...)

 

[SteamKing]

Paul's Online Notes on Variation of Parameters gives some tips about solving this type of ODE:

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

 

[LCKurtz]

Hi there, I know that when I am to guess a solution to to a polynomial for g(t) that I guess Ax^n + Bx^n-1... when the highest power of the polynomial is n but what is my guess supposed to be if the power of n is negative?

ex.
y'' + 4y' + 4y = t^-2*e^(-2t)

so far my guess is,

A*e^(-2t)(B*?...)

To add to SteamKing's link, you don't even try undetermined coefficients if n is negative, because it won't work.