Non-homogeneous 1st order diff equation

  • Thread starter becca1989
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  • #1
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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!

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
rock.freak667
Homework Helper
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Integrate by parts

u=e-30t

dv=20sin(αt)+αcos(αt) dt
 
  • #3
3
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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.
 

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