Solving DE Homework: Non-Unique PI?

[neelakash]

Homework Statement

Given DE is D^2(y)+5Dy+4y=cos 2x ...where D=>(dy/dx)

We are to find the general solution.(I have done it already)
Is the particular integral unique?If not,find another PI and show that the general solution is the same for all PI.

Homework Equations

The Attempt at a Solution

I did the first part and got the general solution as

y=C1 exp(-x)+C2 exp(-4x)+(1/10)cos 2x

I cannot understand why the PI would be non-unique?Can anyone please check if I am correct in having that answer?

 

[HallsofIvy]

?? You might want to check the definition of "particular integral"! They are never unique.

As far as checking is concerned, all you have to do is differentiate! Did you notice that if y= (1/10)cos(2x) then Dy= (1/5)sin(2x) so 5 Dy= sin(2x). How are you going to get rid of that sin(2x) on the left side of the equation?