Method of Undetermined Coefficients

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Homework Help Overview

The discussion revolves around the application of the method of undetermined coefficients to find a particular solution for a differential equation. Participants are evaluating the conditions under which this method is applicable, particularly focusing on the form of the equation and the nature of the forcing function.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss whether the method can be applied based on the structure of the differential equation and the characteristics of the forcing function. There is an exploration of simplifying terms, such as replacing trigonometric expressions with their equivalent values.

Discussion Status

The conversation indicates that some participants believe the method can be applied, while others explore simplifications that could facilitate the process. There is no explicit consensus, but guidance on factoring and simplification has been provided.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may impose specific rules on the methods that can be used. The original poster's question reflects uncertainty about the applicability of the method based on the equation's form.

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Homework Statement
Decide whether or not the method of indetermined coefficients can be applied to find a particular solution of the given equation:

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The attempt at a solution
I think the answer is yes, because the equation is of the form: [tex]a\ddot{y}+b\dot{y}+cy=F(t)[/tex]where F(t) is the sum or product of polynomials, exponentials, sines, cosines.

Am I correct?
 
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Yes it can, you can also factor out the 4x to make it easier since you know what sin2x+cos2 is equal to.
 
Oh so I can replace sin2x+cos2x with 1, which gives me a RHS of simply 4x?
 
Yep.
 

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