Find the general solution for a nonhomogenous equation.

[cyturk]

Homework Statement

Find the general solution for a nonhomogenous equation.
y''+4y=3csc2t

Homework Equations

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-BcostThen 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.

 

[hunt_mat]

Variations of parameters.

 

[cyturk]

Variations of parameters.

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?

 

[rock.freak667]

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

 

[Danny B]

Here is a source that provides a nice shallow learning curve:

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

 

[cyturk]

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