Results 1 to 3 of 3

Math Help - Systems of ODE, using Laplace Transforms

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    12

    Systems of ODE, using Laplace Transforms

    Hi everyone, this is my first post here, but hopefully ill be sticking around and having a bit input!

    Anyways, im revising for the end of year exams and as usual with maths one of the best ways to get good is just to practice, practice practice! For a module on all sorts of Differential Equations, which wouldn't be complete without Laplace transforms, ive been doing just that and hit a snag on one question which i need help with more for the sake of my own sanity than anything else! I think ive just went about it the wrong way, missed the obvious and ended up in an algebraic swamp!

    So say I had to solve

    2x' + 3y' +7x = 14t + 7
    5x' -3y' + 4x + 6y = 14t -14

    given x(0)=y(0)=0 (thankfully!)


    So I take the laplace transforms first off (sorry i havent got the hang of latex yet!) (NB in my notation, the lower case x has changed to X like you may see on paper with a line above it! f(t)=F(s) kinda thing)


    2sX+3sY+7X = 14/s^2 + 7/s
    5sX -3sY +4X +6Y = 14/s^2 -14/s

    Rearanging...

    X(2s+7) +3sY= s(7s+14)/s^3
    X(5s +4) + Y(6-3s)=s(14-14s)/s^3

    Using the first one

    Y=s(7s+14)/3s^4 - X(2s+7)/3s

    And putting it back into the second one.

    I get it down to the stage

    X= (-21s^2 +42s -84 ) /( s^2 (9s^2 +3s -84))

    And its driving me mad!

    I cannot think of any tricks or ways of factorising this!!!! Im willing to bet ive made or have forgot something simple to the point of embarrasment but i am meant to be revising but instead have spent 3 hours on a whiteboard trying to do this, and it is making me feel thick!

    The idea was to get that, factorise so things cancell out quite nicley, mabey do a partial fraction, then do an inverse transform using a standard transform, then use x to find y!

    Can anyone point me in the correct direction or have and ideas.


    Again, sorry that it looks more like matlab code than anything else!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    I didn't work the Algebra myself but here is a maple screenshot of what they should be.

    My guess is you have an algebra error

    Systems of ODE, using Laplace Transforms-capture.jpg

    I have found for me elimination works better that substition

    try multiplying the top equation by

    (6-3s) and the bottom by -3s

    Then add the two.

    I hope this helps.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2008
    Posts
    12
    Thanks TheEmptySet, elimination got there alot quicker. It still should have worked the other way, but i can't find error in algebra! That said, studying for exams so cant spend too long looking at one little problem.


    Anyway, thanks for you're time dude
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. LaPlace transforms
    Posted in the Differential Equations Forum
    Replies: 8
    Last Post: January 28th 2011, 10:38 AM
  2. Laplace transforms
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: March 23rd 2010, 01:21 AM
  3. Laplace Transforms
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: April 27th 2009, 02:27 PM
  4. Laplace Transforms
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 25th 2008, 02:13 PM
  5. Solving Systems Using Laplace Transforms
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 7th 2007, 03:23 PM

Search Tags


/mathhelpforum @mathhelpforum