1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.

    [​IMG]


    I submitted this and it was wrong:>
    [​IMG]
     
    Last edited: Feb 8, 2006
  2. jcsd
  3. Feb 8, 2006 #2

    benorin

    User Avatar
    Homework Helper

    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

    User Avatar
    Homework Helper

    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:
    [​IMG]
    Did i mess up finding my constants?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Confused on why i'm missing this 2nd Order Diff EQ with complex roots!
  1. 2nd order diff eq. (Replies: 1)

Loading...