## anonymous 5 years ago How to use undetermined coefficients for right hand side of this differential equation: y''+y'+8y = t*cos3t + (10t^2 +21t + 9) * sin3t

1. anonymous

This is a large problem to write out online, but you can tackle it by finding the particular solution as such. You can find particular solutions to each of$y''+y'+8y=t \cos 3t$and$y''+y'+8y=(10t^2+21t+9) \sin 3t$and add them to find the particular solution to the whole thing. To find the particular solution for the first equation set,$y_1=(At+B)(C \cos 3 t + D \sin 3t)$and for the second,$y_2=(At^2+Bt+C)(D \cos 3t + E \sin 3t)$Substitute each into your d.e. and find the coefficients. Your particular solution will then be$y_p=y_1+y_1$If you need any further help, let me know.

2. anonymous

you a fan of Nikola Tesla? and all his inventions?

3. anonymous

Thank you so much,lokisan. What I didn't get was, if I should write underdetermined coefficients for both polynomial and trigonometric function or just for trigonometric function -which are in multiplication- [ex. in my textbook (e^t * sint) is written in underdetermined coefficients as [e^t * (A*cost + B*sint)] Now I get i should write for both and look for if there are common coefficients (like if there are two A*D coefficient I could write A to simplify that,hope I got it right.

4. anonymous

You're welcome. Become a fan :D If you get stuck, let me know.

5. anonymous

oktal, you wasting time here and not studying?!

6. anonymous

oktal,yep,for sure!