1. Not finding help here? Sign up for a free 30min 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!

Diff Eq Undetermined Coefficients

  1. Jun 1, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the solution for y"+2y'+5y=(e^x)sinx


    2. Relevant equations



    3. The attempt at a solution

    So far I think I've gotten the solution from the characteristic equation, but I'm having trouble with the particular solution.

    For the characteristic equation solution:
    y"+2y'+5y=0
    r^2+2r+5=0
    Using the quadratic formula r= -1(+/-)2i
    So y=(e^-x)((C1)cos(2x)+(C2)sin(2x)

    For the particular solution I think I'm assuming correctly that y=A(e^x)sin(2x)+B(e^x)cos(2x), or am I not catching a term that can be combined with the complementary solution? Or am I just using the wrong equation all together?
     
  2. jcsd
  3. Jun 1, 2007 #2

    G01

    User Avatar
    Homework Helper
    Gold Member

    In this line: y=A(e^x)sin(2x)+B(e^x)cos(2x), you shouldn't have the 2's inside the trig arguments. Since the RHS of the problem statement has only a sin(x), your "guess" should only include trig functions with x as the argument. You are getting the 2's from the Homogeneous Solution, but in this problem, the H solution, does not affect your "guess" of the particular solution.
     
  4. Jun 1, 2007 #3
    Thanks! I don't know how I overlooked that.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Diff Eq Undetermined Coefficients
Loading...