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Math Help - laplace eqn help

  1. #1
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    laplace eqn help

    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
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  2. #2
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    Quote Originally Posted by :|max View Post
    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
    Where are you stuck? It would help if you showed your working.

    Start with notation .... let LT[x(t)] = X(s) and LT[y(t)] = Y(s), say.

    Now take take the Laplace transform of each differential equation.

    This gives two linear equations in X(s) and Y(s) that need to be solved simultaneously.

    Take the inverse Laplace transform of each resulting solution to get x(t) and y(t).
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