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2nd order nonhomogeneos differential equations with initial conditions

  1. May 16, 2013 #1
    I have a problem which in involves a second order differential equations with imaginary roots and I can seem to know how to finish the problem.

    d^2y/dt^2 +15y =cos 4t+2 sin t

    this is what I got so far


    r^2+15=0 for the homogeneous part

    r=+-(√15)

    Yh=C1cos√15+C2sin√15

    now is where I get stuck
     
  2. jcsd
  3. May 16, 2013 #2

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    You've got to use the initial conditions to solve for C1 and C2 in order to complete the homogeneous solution. Then, you get to find the particular solution for in inhomogeneous equation.
     
  4. May 16, 2013 #3
    yes I know but can you explain how

    i know i need to have a particular solution for cos 4t+2 sin t
    but i don't know how to set up
     
  5. May 16, 2013 #4

    Mark44

    Staff: Mentor

    Problems such as these should be posted in the Homework & Coursework section, not in the technical math sections. I am closing this thread.
     
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