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!

What exactly do they want?

  1. Mar 2, 2007 #1
    1. The problem statement, all variables and given/known data

    Set up but do not solve for the appropriate particular solution yp for the differential equation

    y''+25y=–1xcos(5x)

    using the Method of Undetermined Coefficients (primes indicate derivatives with respect to x).

    In your answer, give undetermined coefficients as A, B, etc.
    2. Relevant equations
    Possible Derivatives
    • sin(x)
    • cos(x)
    • xsin(x)
    • xcos(x)



    3. The attempt at a solution

    This seems like the solution should simply be

    [tex] A*x*sin(5*x)+B*x*cos(5*x)+C*cos(5*x)+D*sin(5*x) [/tex]
     
  2. jcsd
  3. Mar 2, 2007 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What solution are you talking about? The problem said "Set up but do not solve for the appropriate particular solution yp for the differential equation
    y''+25y=–1xcos(5x)
    using the Method of Undetermined Coefficients"

    Normally, to get a solution of the form "x cos(5x)" you would use (Ax+B) cos(5x)+ (Cx+ D) sin(5x). However, in this case cos(5x) and sin(5x) are solutions to the homogeneous equation. Multiply what you would normally use by x: (Ax2+ Bx)cos(5x)+ (Cx2+ Dx)sin(5x).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?