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: Series solution to linear differential equations

  1. Nov 29, 2011 #1
    1. The problem statement, all variables and given/known data

    Given the ODE y''-ty'+y=0 where y(0)=1 and y'(0)=0
    Assume y(t)=Ʃn=0 ( a(n) t^n ) (power series centered at 0)

    find the general form of the solution ( an=f(n) )

    3. The attempt at a solution

    I used the initial conditions to determine the values a0=1 and a1=0

    Determined the recurrence relation a(n+2)= a(n) (n-1) / (n+1)(n+2)

    And found the first six non-zero terms (which was asked for in an earlier part of the question.

    a(0)=1 a(1)=0 a(2)=-1/2! a(3)=0 a(4)=-1/4! a(5)=0 a(6)=-3/6! a(7)=0 a(8)=-15/8! a(9)=0 a(10)=-105/10!

    I am having a really tough time coming up with a(n) I can identify a few patterns such as there is obviously a component 1/n! and since all the odd terms are 0 it would be 1/(n+1)! I attempted to handle the first term being positive and the rest negative using (n-1)/abs(n-1) I am assuming there is a better way to handle this however. I am very lost on coming up with a series representation of the numerator {1-1-1-3-15-105-...-...}

    Any help will be appreciated very much.
    Thanks for your time!
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

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