Results 1 to 3 of 3

Math Help - Power series solution

  1. #1
    Junior Member
    Joined
    Nov 2009
    From
    Australia
    Posts
    56

    Power series solution


    Hi guys,

    May I confirm if my approach is correct so far as I work towards the solution.

    I apologize in advance, it looks a bit long, but it is just the first few steps of the approach (no work on equating coefficients etc yet)

    1) This ODE has a regular singular point at x=0 and so Frobenius Method is used where
    y=\sum_{n=0}^{\infty}a_{n}x^{n+s}?

    2) If 1) is correct, when I try to write it out as a series I obtain 3 series:
    x \sum_{n=0}^{\infty} (n+s-1)(n+s)a_{n}x^{n+s-2} - 2 \sum_{n=0}^{\infty} (n+s)a_{n}x^{n+s-1}  + 9x^5 \sum_{n=0}^{\infty} a_{n}x^{n+s} &= 0
    Which simplifies to:
    \sum_{n=0}^{\infty} (n+s-1)(n+s)a_{n}x^{n+s-1} - \sum_{n=0}^{\infty}  2(n+s)a_{n}x^{n+s-1}  + \sum_{n=0}^{\infty} 9a_{n}x^{n+s+5} &= 0

    May I confirm if this is correct?

    3) My next question is that I attempt to make the summation indexes the same - i.e. n=5. However I get a large number of terms that need to be taken out of the first 2 series - so wanted to confirm if my approach is correct in the first place.

    Thank you for any feedback given
    Linda
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Aug 2011
    Posts
    234
    Thanks
    53

    Re: Power series solution

    2) is correct.
    3) Let n=N-4 and rewrite the last sum, starting from N=4. After, the character "N" can be replaced by the character "n".
    For information : The EDO is one of Bessel kind. Solutions are :
    y = C1 x^(3/2) BesselJ[1/2 , x^3] +C2 x^(3/2) BesselJ[-1/2 , x^3]
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2009
    From
    Australia
    Posts
    56

    Re: Power series solution

    Hi JJacquelin,

    Thank you for taking the time to look at it and confirm my approach.

    I have let n=N-4 and the series solution works out.
    May I just confirm if the solution should be:
    y=c_{1}\cos[x^3] + c_{2}\sin[x^3]?

    Thank you!!!
    Last edited by lindah; September 23rd 2011 at 04:32 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solution of y''-(1+x)y=0 using power series ..
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: February 9th 2011, 02:22 AM
  2. Power Series Solution
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: November 30th 2010, 10:36 PM
  3. power series solution of second order ode
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: April 10th 2009, 10:46 AM
  4. Power Series Solution
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 17th 2008, 01:52 PM
  5. Power Series Solution
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 9th 2008, 09:52 PM

Search Tags


/mathhelpforum @mathhelpforum