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!

Homework Help: Ordinary Differential Equation Series Solution

  1. Nov 17, 2009 #1
    1. The problem statement, all variables and given/known data
    y' = [tex]\sqrt{(1-y^2)
    Initial condition y(0) = 0
    a) Show y = sinx is a solution of the initial value problem.
    b) Look for a solution of the initial value problem in the form of a power series about x = 0. Find coefficients up to the term in x^3 in this series.

    2. Relevant equations

    part a) was Ok.

    3. The attempt at a solution
    This is for my part b attempt.

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

    (cosx)^2 + (sinx)^2 = 1

    [tex]\sum(-1)^ {2n} * (x^ {4n} )}/(2n!)^2[/tex] + [tex]\sum (-1)^{2n} * (x^ {4n+2})/((2n+1)!)^2[/tex] = 1

    I had also tried the general solution series for y and y'. y = a0 + a1x + ... + an*x^n
    y' = a1 + ... + n*an x^n
    Please note the values such as a0, a1, ...an have the nth term as a subscript.

    Maybe I should not be using part a where y=sinx and y'=cosx because I will have even powers when squared always...?

    What series will allow me to evaluate at the x^3 term?

    Last edited: Nov 17, 2009
  2. jcsd
  3. Nov 17, 2009 #2


    Staff: Mentor

    Double posted.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook