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Homework Help: Homogeneous initial value problem

  1. Mar 24, 2014 #1
    1. The problem statement, all variables and given/known data

    4y" + 4y' + 5y = 0
    y(0) = 3
    y'(0) = 1

    2. Relevant equations

    yh = e^ax(c1cosbx + c2sinbx)

    3. The attempt at a solution

    For the roots I got -1/2 + i and -1/2 - i so my a = -1/2 and b = 1

    then I have to differentiate yh = e^(-1/2x)[c1cosx + c2sinx]

    this is where I get this overly complicated equation and I was wondering if I could do integration by parts instead.

    where I could get something like

    yh = -1/2e^(-1/2x)[c1cosx + c2sinx] + [-c1sinx + c2cosx]e^(-1/2x)
    Last edited: Mar 24, 2014
  2. jcsd
  3. Mar 24, 2014 #2


    Staff: Mentor

    Your title is misleading. Your equation is a homogeneous equation.
    You can't use integration by parts if you need to differentiate a function.
  4. Mar 24, 2014 #3
    Damn I'm so sorry I misled you, I've been working on these all day and well you know how that goes. What I meant to say was product rule, where f(x) = e^(-1/2x) and g(x) = [c1cosx + c2sinx]
  5. Mar 24, 2014 #4


    User Avatar
    Homework Helper

    Yes, use product rule for y= e-x/2(c1cosx+c2sinx) to get y'.

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