Results 1 to 2 of 2

Math Help - Solving Systems Using Laplace Transforms

  1. #1
    Junior Member
    Joined
    May 2007
    Posts
    69

    Solving Systems Using Laplace Transforms

    Please help

    Use the Laplace Transforms to solve the initial value problem

    x'= x+ 2y, y'= x+ e^(-t); x(0)= 0, y(0)= 0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by googoogaga View Post
    Please help

    Use the Laplace Transforms to solve the initial value problem

    x'= x+ 2y, y'= x+ e^(-t); x(0)= 0, y(0)= 0
    Let \int_0^{\infty}e^{-st}xdt = F(s) \mbox{ and }\int_0^{\infty} e^{-st}ydt = G(s).

    Then,
    \int_0^{\infty} e^{-st}x' dt = \int_0^{\infty} e^{-st}(x+2y)dt
    \int_0^{\infty} e^{-st}y' dt = \int_0^{\infty} e^{-st}(x+e^{-t})dt

    Thus,
    -x(0)+sF(s) = F(s)+2G(s)
    -y(0)+sG(s) = F(s)+\frac{1}{s+1}
    Thus,
    F(s)(s-1)=2G(s)
    Substitute,
    sG(s) = \frac{2G(s)}{s-1}+\frac{1}{s+1}

    You finish it.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving Laplace transforms from a given, linear graph
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: February 26th 2010, 11:28 PM
  2. Laplace Transforms of DE
    Posted in the Differential Equations Forum
    Replies: 9
    Last Post: August 25th 2009, 10:21 PM
  3. Systems of ODE, using Laplace Transforms
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: May 13th 2009, 01:24 PM
  4. Replies: 5
    Last Post: January 11th 2009, 06:59 PM
  5. Laplace Transforms
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 25th 2008, 01:13 PM

Search Tags


/mathhelpforum @mathhelpforum