Thread: Undetermined Coefficients question

My Yp expression is:



But for this one,

its:


For the second one, the expression for cos(5x) is written as [tex]

but for the first one, sin(9x) its :


Why does the second instance have an x infront of the cos and sin? Whats the rule here?

The rule here is that functions that show up in the homogeneous solution (that is, the differential equation LHS = 0), need to be "enhanced" in order not to be annihilated by the LHS's operator when you plug it into the DE. Notice that in your second yp, there's an x multiplying the exponential. That's because in that case, the exponential is already a part of the homogeneous solution. In the first problem, the trig functions are both in the homogeneous solution. Make sense?

Oh Thank you!
However, when I solve my homo equation for the first one, I get

Which isnt quite whats on the RHS. Does it matter whats inside the cos and sin?

It does matter what's inside the trig functions, and I don't think your homogeneous solution is correct. Check it again, if you would, please.