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

For example:

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!!