Results 1 to 2 of 2

Math Help - Power Series Solution

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    1

    Power Series Solution

    We are given the IVP y'' - xy = e^x , y(0)=1, y'(0)=0 and we are asked to find a recurrence relation and the first four nonzero terms in the power series solution of this IVP. The problem is that all the problems of this type that i have encountered are the homogeneous equations. Here since the RHS is not zero, should we write the Taylor series expansion of e^x and then equate the coefficients after finding the a_2? I did so and found a_2 to be 1/2. Is it right? And what is the solution in case to check my answer? Thanks for your help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    Yes you should express e^x in terms of its power series. It shouldn't be too hard to combine all the series together and so, the question is no different from a homogenous equation.

    \begin{aligned} e^x & = y'' - xy \\ 0 & = y'' - xy - e^x \\ 0 & = \sum_{n=2}^{\infty} n(n-1)c_nx^{n-2} - \sum_{n=0}^{\infty}c_nx^{n+1} - \sum_{n=0}^{\infty} \frac{1}{n!}x^n \\ 0 & = \sum_{n=0}^{\infty}(n+2)(n+1)c_{n+2}x^n - \sum_{n=1}^{\infty} c_{n-1}x^n - \sum_{n=0}^{\infty}\frac{1}{n!} x^n \\ & \ \ \vdots \end{aligned}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Power series solution
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: September 23rd 2011, 04:21 PM
  2. 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
  3. Power Series Solution
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: November 30th 2010, 10:36 PM
  4. power series solution of second order ode
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: April 10th 2009, 10:46 AM
  5. Power Series Solution
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 9th 2008, 09:52 PM

Search Tags


/mathhelpforum @mathhelpforum