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Math Help - laplace

  1. #1
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    laplace

    Hi Guys,
    Could you give my work a quick check... I'm hoping im doing this correctly :0


    Find the solution to the following IVP using Laplace transforms:

    y' + 3y = 2e^-4t with y(0) = 2



    First, take the Laplace transform of both sides:

    L[y'+3y] = L[2e^-4t]

    sL{y} - y(0) + 3L{y} = 2/(s+4)

    L{y} (s + 3) = 2/(s+4) + 2



    taking the inverse laplace transform of both sides.


    2/(s+3)(s+4) = A/(s+3) + B/(s+4)

    A(s+4) + B(s+3) = 2

    s=-4 s=-3
    -B = 2 A = 1

    Therefore, our transform equation becomes:



    Taking the inverse laplace transform of both sides, we get:





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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by boousaf View Post
    Hi Guys,
    Could you give my work a quick check... I'm hoping im doing this correctly :0


    Find the solution to the following IVP using Laplace transforms:

    y' + 3y = 2e^-4t with y(0) = 2



    First, take the Laplace transform of both sides:

    L[y'+3y] = L[2e^-4t]

    sL{y} - y(0) + 3L{y} = 2/(s+4)

    L{y} (s + 3) = 2/(s+4) + 2



    taking the inverse laplace transform of both sides.


    2/(s+3)(s+4) = A/(s+3) + B/(s+4)

    A(s+4) + B(s+3) = 2

    s=-4 s=-3
    -B = 2 A = 1

    Therefore, our transform equation becomes:



    Taking the inverse laplace transform of both sides, we get:






    Your answer is correct. Remember you can always check your work by taking derivatives and pluggin into the equation.
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  3. #3
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    You are indeed correct! Well done!
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  4. #4
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    thanks guys, very much appreciated!
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