Guessing the particular solution

[jdawg]

Homework Statement

Find both a particular solution yp (via the method of educated guess) and a general solution y.
y⁽²⁾-6y⁽¹⁾=25sin(6x)

Homework Equations

The Attempt at a Solution

This was my guess:
yp(x)=Asin(6x)
I then took derivatives, plugged them in, and simplified to get this:
-27Asin(6x)-36Acos(6x)=25sin(6x)
I'm stuck at this point! How do I solve for A? Or did I just make a bad guess for the particular solution?

 

[bigfooted]

you end up with sin and cos terms, so it makes sense to try as particular solution also something with sin and cos terms:
$y_p = A\sin(6x) + B\cos(6x)$

 

[jdawg]

Ohhhh duh, thanks so much!