Second order ODEs- P.Integral for e^xsinx

  • Thread starter Smith987
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  • #1
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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!
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
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The PI would just the the product of the PI for ex and sinx
 
  • #3
AEM
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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!
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.)
 
  • #4
6
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Aha thanks for the help guys :)
 

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