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laplace eqn help

  • 11-08-2008 09:46PM
    #1
    :|
    Registered Users, Registered Users 2 Posts: 960 ✭✭✭


    Hey can anyone tell me the method to solve this, I can do inverse linear eqns and such but i dont know how to solve this type of question:


    Use Laplace transforms to solve the following systems of linear equations

    (a) dx/dt= 3x(t) − 4y(t),
    dy/dt= 2x(t) + 3y(t),

    with initial conditions x(0) = 1, y(0) = 0.


    thanks


Comments

  • #2
    Michael Collins
    Moderators, Science, Health & Environment Moderators Posts: 1,855 Mod ✭✭✭✭Michael Collins


    The 1st one:

    dx/dt = 3 x(t) - 4 y(t)

    So now take Laplace Transform (differentiation corresponds to multiplication by s in the Laplace domain, then minus the initial condition):

    s X(s) - x(0) = 3 X(s) - 4 Y(s)
    s X(s) - 1 = 3 X(s) - 4 Y(s)
    s X(s) - 3 X(s) = 1 - 4 Y(s)
    X(s) [s - 3] = 1 - 4 Y(s)
    X(s) = 1/(s - 3) - 4 Y(s) / (s - 3)

    Now solve the 2nd one in the same way, to get an expression for Y(s), sub this into the above, then take the inverse Laplace Transform.


  • #3
    :|
    Registered Users, Registered Users 2 Posts: 960 ✭✭✭:|


    got it out, thanks for your help :)


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