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Differential Equations - power series method

  1. Apr 24, 2009 #1
    1. The problem statement, all variables and given/known data

    Solve:

    y'' + y' - 2y = 0

    y(0) = 1
    y'(0) = -2

    2. Relevant equations



    3. The attempt at a solution

    I found:

    http://image.cramster.com/answer-board/image/cramster-equation-200942414569633761817696516250247.gif

    So the recurrence relation is:

    http://image.cramster.com/answer-board/image/cramster-equation-20094241457286337618184812037502167.gif

    for n = 0:

    http://image.cramster.com/answer-board/image/cramster-equation-20094241458446337618192469850005024.gif

    Now here's my question. Can I assume at this point that:

    c0 = y(0) = 1
    and c1 = y ' (0) = -2

    ?

    This would allow me to have a numerical value for each cn.

    Thanks!
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Apr 24, 2009 #2

    Mark44

    Staff: Mentor

    Yes. Think about what your original power series for y(x) looked like. All the terms except the first had nonzero powers of x, so if x = 0, you have y(0) = c0. Then, think about what y'(x) looks like. Same idea for c1.
     
  4. Apr 24, 2009 #3
    Thanks Mark. I was able to solve this by making the above assumption getting y(x) = e-2x I just wasn't sure if I was permitted to make that assumption.
     
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