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Confused on why i'm missing this 2nd Order Diff EQ with complex roots!

  1. Feb 8, 2006 #1
    Hello everyone. I"m not getting this problem right. <insert sad face here>
    Find y as a function of t if
    6y'' + 33y = 0,
    y(0) = 8, y'(0) = 5 .
    y(t) =

    hokay, here is my work, it is sloppy sorry. Can you see any obvious mistakes I made? Note: the sqraure root should be encompassing both the 11 and the 2 in 11/2.

    http://img136.imageshack.us/img136/681/lastscan8wk.jpg [Broken]


    I submitted this and it was wrong:>
    http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/90/5f593c3fcc529485c44d6db5c6c1ea1.png [Broken]
     
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Feb 8, 2006 #2

    benorin

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    For your general solution, that is

    [tex]y=Ae^{i\sqrt{\frac{11}{2}}t}+Be^{-i\sqrt{\frac{11}{2}}t}[/tex]

    put now instead

    [tex]y=c_1\sin {\sqrt{\frac{11}{2}}t}+c_2\cos {\sqrt{\frac{11}{2}}t}[/tex]
     
  4. Feb 8, 2006 #3

    benorin

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    that comes from Euler's formula [tex]e^{i\alpha}=\cos\alpha+i\sin\alpha[/tex], substituted into the general solution with the e's, some constant renaming and some trickery to show that if the new solution (with the cos + isin stuff) is a complex solution to the DE, then the same thing without the i is also a solution. But that was mostly hand-waving.
     
  5. Feb 9, 2006 #4
    Thanks for the help again benorin, but I submitted:
    http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/32/eb2319e057d3fc3b2523e3d817a55a1.png [Broken]
    Did i mess up finding my constants?
     
    Last edited by a moderator: May 2, 2017
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