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Math Help - Inverse Laplace

  1. #1
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    Inverse Laplace

    Can someone please help me figure out the inverse Laplace of:

    <br />
\frac {2x^{2s-1}}{s^3(2s-1)}<br />

    Well i know what the inverse of
     <br />
\frac {2}{s^3(2s-1)}<br />
is but i Dont know what to do with the  x^{2s-1}


    Any guidance would be very appreciated
    Thank you
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by gconfused View Post
    Can someone please help me figure out the inverse Laplace of:

    <br />
\frac {2x^{2s-1}}{s^3(2s-1)}<br />

    Well i know what the inverse of
     <br />
\frac {2}{s^3(2s-1)}<br />
is but i Dont know what to do with the  x^{2s-1}


    Any guidance would be very appreciated
    Thank you
    I will take a shot.

    Assume that x \ne 0 and x is NOT a function of s then

    <br />
\frac{2}{x} \cdot \frac {x^{2s}}{s^3(2s-1))}=\frac{1}{x} \cdot \frac{e^{s(2\ln(x))}}{s^3(2s-1)}<br />

    Now this is in the form of a Heaviside function

    I hope this helps.

    \frac{1}{x}\mathcal{U}(t+2\ln(x) \mathcal{L}^{-1}\left( \frac{1}{s^3(2s-1)}\right) \bigg|_{t \to t+2\ln(x)}

    Where

    \mathcal{U}(t-a)=\begin{cases} 0, t < a \\ 1,t>a \end{cases}
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  3. #3
    Junior Member
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    Oh wow thanks, i get it now, you helped me heaps
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