Results 1 to 2 of 2

Math Help - Help required? Solve the Differential equation by the Laplace transform method"

  1. #1
    Newbie
    Joined
    Mar 2011
    Posts
    1

    Help required? Solve the Differential equation by the Laplace transform method"

    Hello

    I wonder if you can help? I believe I'm doing this correctly, but iv got caught up in the algebra. Ill list all the question and then as far as I have got.

    Kind regards
    ----------------------------------------------------------------------
    You are required to solve the following differential equation by the Laplace transform method:

    d^2x/dt^2 + 5*dx/dt - 24x = 4t

    with

    x(0) = 2
    x'(0)=9

    (i)
    Take the Laplace transform of the differential equation and solve the resulting equation for X, the Laplace transform of the solution
    Give your answer as a function of only. Omit the "X ="

    d^2x/dt^2 + 5*dx/dt - 24x = 4t
    Taking the Laplace transform

    L(d^2x/dt^2) + 5L(dx/dt) -24L (x) = 4L(t)

    (s^2X - sx(0)-x'(0)) + 5( sX - x(0)) - 24X = 4/s^2
    Sub in values given within questions for x(0) and x'(0)

    (s^2X - 2s - 9) + (5sX - 10) - 24X = 4/s^2
    Expanding brackets out and collecting like terms

    X(s^2+5s-24) = 4/s^2 + 2s +19
    Factorising LHS

    X((s-3)(s+8)) = 4/s^2 + 2s +19

    I can't see where to go next to, iv looked at brining the (s-3)(s+8) to the RHS but I get muddled with all the numbers and it doesn't seem to look correct.

    Thanks again
    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
    Quote Originally Posted by Davidc2233 View Post
    Hello

    I wonder if you can help? I believe I'm doing this correctly, but iv got caught up in the algebra. Ill list all the question and then as far as I have got.

    Kind regards
    ----------------------------------------------------------------------
    You are required to solve the following differential equation by the Laplace transform method:

    d^2x/dt^2 + 5*dx/dt - 24x = 4t

    with

    x(0) = 2
    x'(0)=9

    (i)
    Take the Laplace transform of the differential equation and solve the resulting equation for X, the Laplace transform of the solution
    Give your answer as a function of only. Omit the "X ="

    d^2x/dt^2 + 5*dx/dt - 24x = 4t
    Taking the Laplace transform

    L(d^2x/dt^2) + 5L(dx/dt) -24L (x) = 4L(t)

    (s^2X - sx(0)-x'(0)) + 5( sX - x(0)) - 24X = 4/s^2
    Sub in values given within questions for x(0) and x'(0)

    (s^2X - 2s - 9) + (5sX - 10) - 24X = 4/s^2
    Expanding brackets out and collecting like terms

    X(s^2+5s-24) = 4/s^2 + 2s +19
    Factorising LHS

    X((s-3)(s+8)) = 4/s^2 + 2s +19

    I can't see where to go next to, iv looked at brining the (s-3)(s+8) to the RHS but I get muddled with all the numbers and it doesn't seem to look correct.

    Thanks again
    So far your algebra looks correct and your idea is sound. You need to isolate X(s)

    This gives
    \displaystyle X(s)=\frac{4}{s^2(s-3)(s+8)}+\frac{2s}{(s-3)(s+8)}+\frac{19}{(s-3)(s+8)}

    Now you need to use partial fraction decomposition on the RHS side. Then you will be able to find the inverse transform.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving a differential equation using Laplace transform
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: November 22nd 2011, 05:47 PM
  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. Solve second order differential equation by Laplace transform
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: October 11th 2011, 05:48 PM
  4. Using Laplace Transform to solve Differential equations
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: April 10th 2011, 02:44 AM
  5. Differential equation-Laplace Transform
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 19th 2008, 07:50 AM

/mathhelpforum @mathhelpforum