# Homework Help: 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 :)