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Math Help - Please help me use Laplace to solve this system of equations!

  1. #1
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    Please help me use Laplace to solve this system of equations!

    ; x(0)=o, x'(0)=2, y(0)=0


    Thank you for helping me understand how to solve this system of equations!!!
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Bananna View Post
    ; x(0)=o, x'(0)=2, y(0)=0


    Thank you for helping me understand how to solve this system of equations!!!
    Here is the first one

    Taking the transform of both sides gives

    s^2X-2+3sY+3Y=0

    and
    s^2X-2+3Y=\frac{1}{(s+1)}

    Now we have a system of Algebraic equaions. So isolate Y is the 2nd equation to get

    3sY=-\frac{1}{s+1} \iff Y= -\frac{1}{3}\left( \frac{1}{s(s+1)}\right)

    Taking the inverse transform (by any method you know)

    Here is using the convolution theorem we get

    y(t)=-\frac{1}{3} \int_{0}^{t}e^{-\tau}d\tau=-\frac{1}{3}\left( -e^{-t}+1\right)

    This should get you started. Good luck.
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  3. #3
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    You got me just where I needed to be, that wasn't difficult thanks for the help!
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