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Second order differential equation

  1. Apr 26, 2010 #1
    show that y1(x) = e^(2+i)x and y2(x) = e^(2-i)x, i=sqrt(-1) are two linearly independent functions

    hence obtain a second order linear differential equation with constant coefficients each that y1(x) and y2(x) are its two fundamental solutions.

    my attempt :

    for the first part, I use the definition of wroskian = y1y2'-y2y1' and show it not equal to zero... ok

    the second part, I don't know how to do it...

    how to get the second order differential equation????

    is that setting : (r+2+i)(r+2-i) to get the auxillary equation??? is that possible??? can someone show me to solve this problem???:confused:
  2. jcsd
  3. Apr 26, 2010 #2
    If you want that auxiliary equation, what will be the differential equation? When you get it, you can check whether the two original functions satisfy it.
  4. Apr 26, 2010 #3
    how to do that... still blurr...
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