Question

Need help please! y"-2y'+y=2e^x-3e^-x
Solve second order differential. Thanks!

Answer 1

Grr I always get confused by Variation of Parameters :(
It's been so long...

Did you find the solution to the homogeneous part of the equation?

Answer 2

yes, apparently this one cant be done with variation, has to be undetermined coefficients

Answer 3

Im not sure why, but a friend told me that just now.

Answer 4

use this as guess:
\[y = x^2 e^x + Be^{-x}\]
differentiate y' and y''
plug into y'' -2y' +y = 2e^x -3e^-x
solve for B
**the x^2 terms should cancel out

Answer 5

why did you use \[x^2\]?

Answer 6

why didnt you put A there

Answer 7

because e^x and x e^x are homogenous solutions. thus, your guess needs to be of the form a x^2 e^x + b e^(-x)