1. ## Nonhomogeneous equation

Can someone show how to solve:

y'' + 9y = sin^4(x)

2. First find the charateristic equation to the homogeneous equation and solve it.

y'' + 9y = 0

gives

r^2 + 9 = 0

Now solve this guy, you should get complex solutions. What does this mean?

3. Got that.
yc(x) = c1cos3x + c2sin3x

I get duplication tho right? what do I do from here?

4. Originally Posted by jzellt
Got that.
yc(x) = c1cos3x + c2sin3x

I get duplication tho right? what do I do from here?
To get a particular solution, note (using the usual double angle formulae) that $\displaystyle \sin^4 (x) = -\frac{1}{2} \cos (2x) + \frac{1}{8} \cos (4x) + \frac{3}{8}$.