1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Complexification of rsin(at)+rcos(at)

  1. Mar 1, 2009 #1
    Sorry for this dumb questions! its that i am just trying to find multiple ways of solving problems: Basically i have

    y'' + 9y' = 648sin(9 t) + 648cos(9 t)

    i dont know how can you complexify this, would it be p(D)y=648exp(9t)?

    if so, what part do i extract, the imaginary or real? because it has both....

    i can solve this with uknown coefficients but i am trying to look for efficient ways of doing this.
  2. jcsd
  3. Mar 1, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper


    Hi marmot! :smile:

    Do you mean y'' + 9y' = i648sin(9 t) + 648cos(9 t)? :confused:

    (and do you mean 3t?)

    if so, yes, that's 648ei9t
  4. Mar 1, 2009 #3
    no, it lacks the imaginary number, its just like that. i am trying to complexify it so that the differential equation becomes relatively straightforward. the problem i encounter is that generally when i want to complexify something, its either sin(x) or cos(x) that is in the right of the equation, not both. so i am wondering how to complexify it and then, whether if i have to extract from the solution the real or imaginary or both parts.

  5. Mar 1, 2009 #4

    Ben Niehoff

    User Avatar
    Science Advisor
    Gold Member

    You need both [itex]e^{i\omega t}[/itex] and its complex conjugate.
  6. Mar 1, 2009 #5
    I would rewrite the right hand side in the form R*cos(9t+a), where R and a are two new constants, because then it is the real part of R*e^i(9t+a).
  7. Mar 1, 2009 #6
    thank you!

    however marmoset

    i am trying to do this


    where p(D)=D^2+D


    the solution would be


    however, how can i do this when i have two unknown variables, which in your case, are R and a?
  8. Mar 1, 2009 #7
    Last edited: Mar 2, 2009
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook