Here is the problem:
y''-10 y' +25y = -16 e^(5t)
And I am trying to find the particular solution!
I tried using the method of undetermined coefficients but no matter what my initial guess of Yp(x) I always get 0 on the left side
Yp(x) = Axe^(5x)
Y'p(x) = A(5x+1)e^(5x)
y''p(x) = A(25x+10)e^(5x)
Then I substitute into the original function
and I get:
(25AX-50AX+25AX+10A-10A)e^(5x) = -16 e^(5x)
-> 0(e^(5x) = -16 e^(5x)
then I don't know what to do anymore...
Did I do something wrong or I should use a different method to approach this problem?
Thank you for the help!!