Results 1 to 4 of 4

Math Help - Solve second order differential equation by Laplace transform

  1. #1
    Junior Member
    Joined
    Aug 2010
    Posts
    41

    Solve second order differential equation by Laplace transform

    I am trying to solve the following equation using Laplace method

    ty" + (4t-2)y' - 4y = 0; y(0)=1 and y'(0)=constant

    I have not come across a problem in this form (specifically the 4t-2), thus I am confused as to how I should begin the problem. Any pointers leading me in the correct direction would be much appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: Solve second order differential equation by Laplace transform

    Quote Originally Posted by cheme View Post
    I am trying to solve the following equation using Laplace method

    ty" + (4t-2)y' - 4y = 0; y(0)=1 and y'(0)=constant

    I have not come across a problem in this form (specifically the 4t-2), thus I am confused as to how I should begin the problem. Any pointers leading me in the correct direction would be much appreciated.
    Take the Laplace transform of each term. Where are you stuck in doing this? Note that (4t-2)y' can be re-written as 4ty' - 2y' ....
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Aug 2010
    Posts
    41

    Re: Solve second order differential equation by Laplace transform

    Yes, but I am unsure what to do with a variable in front of the differentials.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2

    Re: Solve second order differential equation by Laplace transform

    Multiplication by t corresponds to the negative derivative in the s domain. See here. So it looks to me as though the LT is going to reduce the order of your DE by one, instead of reducing it to an algebraic equation altogether.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Basic Laplace Transform of a 1st order Differential Equation
    Posted in the Differential Equations Forum
    Replies: 12
    Last Post: October 14th 2011, 12:57 AM
  2. Laplace Transform of a 2nd order Differential Equation
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: October 13th 2011, 03:18 AM
  3. Using Laplace Transform to solve Differential equations
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: April 10th 2011, 02:44 AM
  4. Replies: 1
    Last Post: March 6th 2011, 07:41 AM
  5. Replies: 2
    Last Post: February 23rd 2009, 06:54 AM

Search Tags


/mathhelpforum @mathhelpforum