Second order ODEs- P.Integral for e^xsinx

1. Jan 12, 2010

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!

2. Jan 12, 2010

rock.freak667

The PI would just the the product of the PI for ex and sinx

3. Jan 12, 2010

AEM

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.)

4. Jan 17, 2010

Smith987

Aha thanks for the help guys :)