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Math Help - Piecewise Laplace 2

  1. #1
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    Piecewise Laplace 2

    y'' + 2y' -35y = T(t)

    Where T(t) =

    1 from 0 to 1
    0 from 1 to infinity

    y'(0) = 0, y(0) = 0

    part 1:

    Y(s) = ?

    After taking Laplace of both side I get

    (s^2-2s-35)Y(s) = 1/s
    Y(s) = (1/s)(1/(s^2-2s-35))

    but it's wrong...

    and second part

    Find the inverse transform to find y(t)

    How would I approach that?

    Thank you!!!
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  2. #2
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    Quote Originally Posted by Phyxius117 View Post
    y'' + 2y' -35y = T(t)

    Where T(t) =

    1 from 0 to 1
    0 from 1 to infinity

    y'(0) = 0, y(0) = 0

    part 1:

    Y(s) = ?

    After taking Laplace of both side I get

    (s^2-2s-35)Y(s) = 1/s
    Y(s) = (1/s)(1/(s^2-2s-35))

    but it's wrong...

    and second part

    Find the inverse transform to find y(t)

    How would I approach that?

    Thank you!!!
    T(t) = H(t) - H(t - 1) where H(t) is the Heaviside Step function: Heaviside step function - Wikipedia, the free encyclopedia
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