Solve y''-y=cot(x).

I started solving this thinking it was a first order differential (which I am pretty sure I could solve) then I noticed it was a second order and I'm lost.

Question

Solve y''-y=cot(x).

I started solving this thinking it was a first order differential (which I am pretty sure I could solve) then I noticed it was a second order and I'm lost.

anonymous · Answer

You have your characteristic equation,
$$r^2-1=0$$
with roots $r=\pm1$, so you have the general (homogeneous) solution
$$y_h=C_1e^x+C_2e^{-x}$$
Have you tried solving using variation of parameters?

anonymous · Answer

no not yet. He has been out of class for two weeks and this was the homework assignment left.

anonymous · Answer

Have you at least learned about VoP? I wouldn't want to delve into the details of something you're not familiar with.

anonymous · Answer

No we haven't I'm sorry. We really only had about a week and a half of class before he was out for medical reasons.

dan815 · Answer

no vop then... undetermined coeff

dumbcow · Answer

http://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx

dumbcow · Answer

why were you given this problem? it doesn't have a clearly defined particular solution http://www.wolframalpha.com/input/?i=y%27%27+-+y+%3D+cot%28x%29

anonymous · Answer

that's a good question. I wonder if he mistyped and meant it to be a first order diff eq because that I really think I could solve.