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ODE and BVP need help

  1. Apr 23, 2007 #1
    how would i find the exact solution to:

    y''(x) +y(x)=0

    with BC's of:

    y(1)+y(-1)=0

    y'(1)+y'(-1)=2

    a little confussing because the BC's I am used to dealing with are like:
    y(0)=0
    y(1)=0
     
  2. jcsd
  3. Apr 24, 2007 #2

    HallsofIvy

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    You really have to think a little. You know, I hope, that the general solution to y"+ y= 0 is y(x)= Ccos(x)+ Dsin(x) so that y'(x)= -Csin(x)+ Dcos(x). Now put those functions into your boundary conditions:
    y(1)+ y(-1)= Ccos(1)+ Dsin(1)+ Ccos(-1)+ Dsin(-1)= 0
    y'(1)+ y'(-1)= -Csin(1)+ Dcos(1)- Csin(-1)+ Dcos(-1)= 2.
    Using the fact that cosine is an even function and sine is an odd function will simplify these a lot.

    Didn't we just do this in another thread?
     
  4. Apr 24, 2007 #3

    I see where I was messing up. I found y(1),y(-1),y'(1) & y'(-1) but I was trying to plug the boundry conditions into these equations instead of pluging these into my boundry conditions. Thanks for the insight.
     
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