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DE Boundary Condition Problem

  1. Oct 15, 2011 #1
    I'm asked to determine if for the solution
    [tex]y=c_{1}e^{x}cos(x)+c_{2}e^{x}sin(x)[/tex]
    for:
    [tex]y"-2y'+2y=0[/tex]

    whether a member of the family can be found that satisfies the boundary conditions:
    [tex]y(0)=1[/tex], [tex]y'(\pi)=0[/tex]

    Not quite sure what to do here. The examples in my book give boundary conditions for the same function, not derivatives.

    When I put the first condition into y, I got c1=1, then substituting that result into the derivative condition I found c2=-1. So I found the constants, does this mean that there is a member of the family that can satisfy the boundary condition? For some reason I think there should be a Wronskian involved.
     
  2. jcsd
  3. Oct 16, 2011 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, there is a member of the family that satisfies the boundary condition and you found it:
    [tex]y(x)= e^x cos(x)- e^x sin(x)[/tex]
     
    Last edited: Oct 16, 2011
  4. Oct 16, 2011 #3
    Alright, thanks for the help!
     
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