Second order ODEs- P.Integral for e^xsinx

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Homework Help Overview

The discussion revolves around finding the particular integral for the second-order ordinary differential equation (ODE) given by f'' + 5f' + f = e^x sin(x). Participants are exploring methods to approach this problem, particularly focusing on the combination of exponential and sinusoidal functions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to find the particular integral and seeks guidance on general strategies for combinations of polynomials, exponentials, and sinusoidal functions. Some participants suggest using the Method of Undetermined Coefficients and propose a specific form for the particular integral involving both sine and cosine terms.

Discussion Status

The discussion is active, with participants offering suggestions and methods for approaching the problem. While there is no explicit consensus, guidance has been provided regarding the use of a specific form for the particular integral and the method to substitute it into the differential equation.

Contextual Notes

The original poster indicates a lack of familiarity with the topic, and there may be assumptions regarding the level of knowledge expected in the discussion. The mention of the Method of Undetermined Coefficients suggests a focus on introductory concepts in differential equations.

Smith987
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Hi guys, I really have no idea how to approach finding the particular integral for, say:

f'' + 5f' + f= e^x sinx

Could anyone help me? And for future reference how do you go about finding the PI for any combination of polynomials/exponentials/sinusoidals?

Thanks in advance for the help!
 
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The PI would just the the product of the PI for ex and sinx
 
Smith987 said:
Hi guys, I really have no idea how to approach finding the particular integral for, say:

f'' + 5f' + f= e^x sinx

Could anyone help me? And for future reference how do you go about finding the PI for any combination of polynomials/exponentials/sinusoidals?

Thanks in advance for the help!

Have you ever heard of the "Method of Undetermined Coefficients"? It is covered in introductory differential equations textbooks.

You might try setting

[tex]f = A e^x sin(x) + B e^x cos(x)[/tex]

and substituting it into your DE. Then collect like terms and see what values A and B have to be in order to make the resulting expression true. ( Hint: the combination of coefficients in front of the cosine terms will have to equal zero.)
 
Aha thanks for the help guys :)
 

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