Question

Undetermined Coefficients trouble

Answer 1

find the general solution of

y" = 4y = 3sin(2t)


i can find the complentary equation no problem

but i am having trouble finding by 'guess' for the particular solution

when i try Acos(2t) + Bsin(2t) as my guess, i get:
0 = 3sin(2t)

so what would my next be?

wolfram alpha says that the particular solution is \[-\frac{ 3 }{4 }tcos(2t)\]
so is the correct guess just Atcos(2t)? and how do i justify making that guess?

Answer 2

hey, I have a table of guessing. Do you want it? I will send you

Answer 3

i think i figured it out actually!

since my complimentary solutions were equivalent to my guesses, i needed to add a 't' to my guess

thanks though