Non-homogeneous 1st order diff equation

[becca1989]

Homework Statement

Hi, I have to solve the following differential equation and while I can get the complimentary function I can't get the particular integral.

y'+30y=20sin(alpha*t)+alpha*cos(alpha*t)

Homework Equations

How do I integrate the product of e^30t and alpha*cos(alpha*t) in order to find the particular integral?

The Attempt at a Solution

I've got y=Ce^(-30t) as the complimentary function but can get no further. Any help would be brilliant, thanks!

 

[rock.freak667]

Integrate by parts

u=e^-30t

dv=20sin(αt)+αcos(αt) dt

 

[becca1989]

Thanks, yeah I've been trying to do it by parts for the last little while but it get's very messy, very quickly whenever I have to integrate by parts twice. I'm rubbish at calculus, I end up with the same solution but it's obviously even near being correct.