# Homework Help: Find the general solution for a nonhomogenous equation.

1. Jun 26, 2011

### cyturk

1. The problem statement, all variables and given/known data
Find the general solution for a nonhomogenous equation.
y''+4y=3csc2t

2. Relevant equations

3. The attempt at a solution
I simplified the equation to...
y''+4y=(3)/(sin(2t))

Then I guessed...
y=Asint+Bcost
y'=Acost-Bsint
y''=-Asint-Bcost

Then I got...
-Asint-Bcost+4Asint+4Bcost=(3)/(sin(2t))

Simplifies to...
3Asint+3Bcost=(3)/(2sintcost))

NOTE: Trig Identity: sin(2t)=2sintcost

I am stuck and I am not even sure if I took the correct steps.

Last edited: Jun 26, 2011
2. Jun 26, 2011

### hunt_mat

Variations of parameters.

3. Jun 26, 2011

### cyturk

Thanks for your help! I have been trying to figure out Variation of Parameters and I can't seem to find it on Khan Academy. Any chance there are any videos or resources you can suggest?

4. Jun 26, 2011

### rock.freak667

http://en.wikipedia.org/wiki/Variation_of_parameters" [Broken] is always a good place as sometimes they'll give an example...like in what I posted.

Last edited by a moderator: May 5, 2017
5. Jun 26, 2011

### Danny B

6. Jun 26, 2011

### cyturk

Thanks for everyone's help! I got a solution, although it kinda looks weird, but it makes sense to me now! :)