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!

Second order nonhomogeneous ODE

  1. Oct 16, 2013 #1
    1. The problem statement, all variables and given/known data

    y''+3y'+3.25=3cost-1.5sint


    2. Relevant equations
    yh = e(a/2)t(Acost+Bsint)
    yp = Kcos(ωt)+Msin(ωt) [when r(x)=kcos(ωt) or ksin(ωt)]


    3. The attempt at a solution

    I got the homogeneous solution, which is e-1.5t(Acost+Bsint)
    but I am having trouble with the particular solution.

    I tried the above equation, making yp=K1cos(ωt)+M1sin(ωt)+K2cos(ωt)+M2sin(ωt)
    since there are 2 trig functions as r(t).
    I couldn't solve for the variables by plugging into the original equation because I was left with 4 variables and only 2 equations.

    EDIT: realized I wasn't consistent with my independent variable, made them all t's instead of t's and x's
     
    Last edited: Oct 17, 2013
  2. jcsd
  3. Oct 16, 2013 #2
    K1cos(ωx) + K2cos(ωx) = (K1 + K2)cos(ωx). Having two sin/cos functions is redundant, since they are linear combinations (in this case, they are the same function, entirely).
     
  4. Oct 17, 2013 #3
    Ah I get it now. I solved for the values (M1+M2) and (K1+K2) instead of the variables individually and got the right answer. Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Second order nonhomogeneous ODE
Loading...