# Homework Help: Quick ODE question

1. Apr 26, 2010

### stanli121

1. The problem statement, all variables and given/known data

y'' + 9y' = cot(3t)

2. Relevant equations

3. The attempt at a solution

This is a linear second order ODE where y(t) and that's what I'm solving for. Can this be solved via an integrating factor or does the cot(3t) part make that invalid? Any help is appreciated.

2. Apr 26, 2010

### Dustinsfl

You can solve the complementary homogeneous equation and then the nonhomogeneous equation.

$y''+9y'=0\Rightarrow m^2+9m=0\Rightarrow m(m+9)=0$ $m=0,-9$

$$y_c=C_1+C_2e^{-9t}$$

Now to form the $y_p$ equation, you need to identify what annihilates cos(3t). Do you know what does?

3. Apr 26, 2010

### LCKurtz

Good luck on that, that's a cotangent, not a cosine. I would suggest variation of parameters.

4. Apr 26, 2010

### stanli121

I don't really know how to solve this equation. My first (and only) attempt at the solution is an integrating factor and that doesn't work. I'm not well versed in differential equations because I haven't gotten there yet in the math sequence.

5. Apr 26, 2010

### LCKurtz

You are probably getting a bit ahead of yourself. Integrating factors are used in the first order equations. Your equation is second order and is solved by methods in the "Constant Coefficient" section of your text. There you will learn about solutions to the homogeneous equation and how to find particular solutions to the non-homogeneous equation.