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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
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

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This 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.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you a fan of Nikola Tesla? and all his inventions?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thank 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.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You're welcome. Become a fan :D If you get stuck, let me know.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oktal, you wasting time here and not studying?!
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