Where Did I Go Wrong With Undetermined Coefficients for y+y'+4y = 2sinh(T)?

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Discussion Overview

The discussion revolves around the application of the method of undetermined coefficients to solve the differential equation y'' + y' + 4y = 2sinh(T). Participants explore different approaches to finding a particular solution and express challenges encountered in the process.

Discussion Character

  • Homework-related, Exploratory, Technical explanation

Main Points Raised

  • One participant mentions solving the homogeneous part but struggles with the non-homogeneous equation.
  • Another participant suggests that the initial guess of the form aE^t + Be^-t is acceptable.
  • A different participant questions the need for further inquiry and encourages testing the proposed guess in the equation.
  • One participant indicates that they attempted an alternative guess involving hyperbolic functions but still obtained an incorrect result.
  • A suggestion is made to post the work in the "Homework" forum to seek specific guidance on the errors encountered.

Areas of Agreement / Disagreement

There is no clear consensus on the correct approach, as participants express differing opinions on the validity of the guesses and the methods to be used. The discussion remains unresolved regarding the specific errors in the application of the method.

Contextual Notes

Participants have not fully detailed their assumptions or the steps taken in their calculations, which may contribute to the confusion. There is also a lack of clarity on how the proposed forms relate to the original equation.

Who May Find This Useful

Students and individuals seeking assistance with differential equations, particularly those using the method of undetermined coefficients and hyperbolic functions.

SoulofLoneWlf
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i solved homogenous but
y"+y'+4y = 2sinh(T)
is giving me trouble
also have a hint
sinh t = (e^t - e^-t)/2

also my "guess" was
aE^t +Be^-t=Y
maybe my guess was wrong?
 
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That should be fine.
 
Why are you asking? Have you tried putting that into the equation? If you are used to working with hyperbolic functions directly, you can also use y= C cosh(t)+ D sinh(t).
 
tried this guess but yield wrong answer guess ill do a few more times thanks all
 
In the "Homework" forum, you can put in your work with wrong answer, and ask where you went wrong.
 

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