Differential Equation Method OF UNDETERMINED COEFF

[FahimP]

Homework Statement

I have been trying to solve this differential equation by Method of Undetermined Coefficients for a long time.

y"-2y'-3y=-3te^(-t) ......

We are supposed to guess a solution then differentiate and go from there. I guessed
y = (At + B)e^(-t) .... but this does not work. ... can someone help me on this ... I have also tried y = Ae^(-t) but this also doesn't work. Is it possible the book answer is wrong ?

Homework Equations

The Attempt at a Solution

 

[vela]

You first need to solve the homogeneous equation. What solution do you get to that?

 

[LCKurtz]

Homework Statement

I have been trying to solve this differential equation by Method of Undetermined Coefficients for a long time.

y"-2y'-3y=-3te^(-t) ......

We are supposed to guess a solution then differentiate and go from there. I guessed
y = (At + B)e^(-t) .... but this does not work. ... can someone help me on this ... I have also tried y = Ae^(-t) but this also doesn't work. Is it possible the book answer is wrong ?

Of course it's possible the book is wrong. It is also possible that you are wrong. You shouldn't have to "guess" what to try if you have the complementary solution.

I suggest you re-check your work for Ae^-t. And if you get an answer you can always check it for yourself by plugging it into the DE.