- #1

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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!

- Thread starter Smith987
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- #1

- 6

- 0

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!

- #2

rock.freak667

Homework Helper

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The PI would just the the product of the PI for e^{x} and sinx

- #3

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

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!

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

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Aha thanks for the help guys :)

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