How to find a particular solution for this using method of undetermined coefficients:
y'' - y = e^(-x) cos( 4 x )
I have got the homogenious equation as:
y = A*e^(1*x) + B*e^(-1*x)
But now am not sure how to get a particular solution with the right side?
Sometimes a DE book will have a list of trial particular solutions.
In this case, we use
Because our problem is of that form. Suppose we would've had
, then we would use
But, back to your problem.
Find the second derivative:
Sub them into the equation and get:
Now, equate coefficients:
There is no sin on the right so that is 0:
A particular solutions is:
A general solution is: