Thread: Nonhomogeneous equation

Can someone show how to solve:

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

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?

Got that.
yc(x) = c1cos3x + c2sin3x

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

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 .