Results 1 to 2 of 2

Math Help - Analytically solving ODEs with non-constant coefficients for a specific t

  1. #1
    Newbie
    Joined
    Dec 2011
    Posts
    1

    Analytically solving ODEs with non-constant coefficients for a specific t

    Given an ODE in the form of f(t)y''+g(t)y'+h(t)y=0

    Since the coefficients are functions of t in order to find a solution for all t this would need to be done numerically. But If all I am looking for is the y(t) at a specific value of t and NOT the general solution, can I just plug in that value of t into the coefficients of the original ODE and then solve it using standard analytically techniques or is a numeric solution the only way?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2

    Re: Analytically solving ODEs with non-constant coefficients for a specific t

    Quote Originally Posted by thesteve View Post
    Given an ODE in the form of f(t)y''+g(t)y'+h(t)y=0

    Since the coefficients are functions of t in order to find a solution for all t this would need to be done numerically. But If all I am looking for is the y(t) at a specific value of t and NOT the general solution, can I just plug in that value of t into the coefficients of the original ODE and then solve it using standard analytically techniques or is a numeric solution the only way?
    Actually, if the functions f(t), g(t), and h(t) have relatively standard Taylor series expansions, you could attempt a series solution. You cannot just plug in one valur of t in order to find y(t) at just that one point, for several reasons. 1. Merely by writing y'(t), you are writing a limit. Limits don't care what happens at a point, they care what happens near a point. Hence, you must have information near that point. 2. You have specified no initial conditions. The DE you wrote down, a linear second-order homogeneous ODE, has two arbitrary constants in its solution (due to the two integrations you are essentially performing) which must be determined by initial conditions. Therefore, there is no way to pin down the solution to the DE, even if you could exhibit it, because it would have two arbitrary constants.

    Do you have a specific f(t), g(t), and h(t) in mind? If so, why not post them?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Second order ODE with non-constant coefficients
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: October 21st 2011, 08:39 PM
  2. Homogenous D.E. with Non-Constant Coefficients
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: October 12th 2011, 09:42 PM
  3. 2nd order DE's with constant coefficients.
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: January 9th 2011, 08:19 AM
  4. solving a tricky infinite limit analytically
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: May 31st 2010, 09:28 AM
  5. ODE - constant coefficients
    Posted in the Calculus Forum
    Replies: 9
    Last Post: December 28th 2008, 08:46 AM

Search Tags


/mathhelpforum @mathhelpforum