Second order ODEs- P.Integral for e^xsinx

[Smith987]

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!

 

[rock.freak667]

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

 

[AEM]

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

$$f = A e^x sin(x) + B e^x cos(x)$$

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.)

 

[Smith987]

Aha thanks for the help guys :)