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Homework Help: Second derivative of e^x minus e^x

  1. Jun 28, 2008 #1
    1. The problem statement, all variables and given/known data
    Show that y(t) = e^t is a solution of y'' - y = 0,

    2. Relevant equations
    integral of e^x dx = e^x +c
    derivative of e^x = e^x



    3. The attempt at a solution
    set m = d(e^t)/dt, which also = e^t then dm = e^t

    then d(m)/dt = e^t if y(t) = e^t is a solution
    integrate both sides m= e^t +c
    substitute e^t = e^t + c which is true for C = 0
    not sure if it is that simple
     
  2. jcsd
  3. Jun 28, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    It's even more simple than that. Put y=e^t. y'=e^t. y''=e^t. y''-y=e^t-e^t=0. You don't need to say much more than that.
     
  4. Jun 28, 2008 #3
    Thanks Dick! sometimes it just helps to be able to ask someone else to look at it.
     
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