Find the general solution for a nonhomogenous equation.

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Homework Help Overview

The discussion revolves around finding the general solution for a nonhomogeneous differential equation of the form y'' + 4y = 3csc(2t). The original poster attempts to simplify the equation and explore potential solutions using trigonometric identities.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the method of variation of parameters and share resources for further learning. The original poster expresses uncertainty about their approach and whether they have taken the correct steps in their solution attempt.

Discussion Status

Some participants provide helpful resources and links related to the method of variation of parameters. The original poster indicates they have reached a solution, though they find it somewhat unconventional. There appears to be ongoing exploration of the topic without a clear consensus on the best approach.

Contextual Notes

The original poster notes a struggle with the method of variation of parameters and seeks additional resources for clarification. There is an acknowledgment of potential confusion regarding the steps taken in solving the equation.

cyturk
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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.
 
Last edited:
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Variations of parameters.
 
hunt_mat said:
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?
 
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.
 
Last edited by a moderator:
Thanks for everyone's help! I got a solution, although it kinda looks weird, but it makes sense to me now! :)
 

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