Results 1 to 3 of 3

Math Help - Find two power series solutions.

  1. #1
    Senior Member
    Joined
    Aug 2009
    Posts
    349

    Find two power series solutions.

    ok i have a problem, that i cant seem to get started on...

    so here is the problem..

    after substituting into a differential equation, the resulting equation is given below. find two power series solutions. list at least 5 non-zero terms in each sequence before using the....



    im thinking that i just substitute different values for k to find the first five terms? is this right? or am I off in my approach?


    any thoughts or assistance would be greatly appreciated...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Each coefficient of x^k is equal to 0

    k=0 => 2c_0+2c_2=0
    k=1 => 5c_1+2c_2-6c_3 = 0
    k=2 => 8c_2+6c_3-12c_4 = 0
    and so on

    You can see that choosing the first 2 coefficients gives all the coefficients
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Aug 2009
    Posts
    349
    Quote Originally Posted by running-gag View Post
    Each coefficient of x^k is equal to 0

    k=0 => 2c_0+2c_2=0
    k=1 => 5c_1+2c_2-6c_3 = 0
    k=2 => 8c_2+6c_3-12c_4 = 0
    and so on

    You can see that choosing the first 2 coefficients gives all the coefficients
    ok i dont see how the x^k on the end will cancel out for the different values of k, maybe at k=0, but as k values increase im not sure they will cancel out...

    can you please explain further?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Power Series Solutions of linear DE
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: March 19th 2010, 06:07 AM
  2. power series solutions
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: June 12th 2009, 08:19 AM
  3. power series solutions
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: June 6th 2009, 10:41 PM
  4. Power Series Solutions of ODE's
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 22nd 2008, 11:58 AM
  5. Power series solutions to ODE
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 30th 2007, 11:50 PM

Search Tags


/mathhelpforum @mathhelpforum