1. Limited time only! Sign up for a free 30min personal 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!

Series Solution Near an Ordinary Point

  1. Apr 12, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine φ''(x0), φ'''(x0), and φ(4)(x0) for the given point x0 if y=φ(x) is a solution of the given initial value problem.

    y'' + (sinx)y' + (cosx)y = 0 y(0) = 0; y'(0) = 1

    2. Relevant equations
    y = φ(x) = Ʃan(x-x0)n

    3. The attempt at a solution
    I started off by differentiating y to get y' and y''. I then plugged those into the original equation, adjusted the numbers a bit to get the entire equation to fit into one summation. From there, I factored out xn, then set the bulk of the equation equal to 0. From there, I solved for an+2, plugged in n=0 to get:

    a2 = (-(sinx)a1 - (cosx)a0))/2

    This is where I get stuck. I am unsure as to what I'm supposed to do from here, although I have ideas. Am I just supposed to somehow solve for a2 and plug it into the φ''(x) equation? If so, where do I get a1 and a0 from?



    Also, I apologize for not knowing how to do the graphic code to make it look as it looks on paper. Thank you!


    UPDATE: Assuming I am correct, I have solved for a2, a3, and a4 when setting a0 = y(0) and a1 = y'(0).
    How do I use these newfound numbers to solve for the solutions?

    a2 = 0
    a3 = -1/6
    a4 = 0
     
    Last edited: Apr 12, 2012
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Series Solution Near an Ordinary Point
Loading...