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Non-homogeneous laplace

  1. Jan 18, 2008 #1
    Hi, I can solve homogeneous laplace fine, but with RHS i get stuck half way through.

    y' +3y = 8e[tex]^{t}[/tex]
    y(0) = 2

    Working as if it was homogeneous..

    sY(s) - 2 + 3Y(s) = 8 . [tex]\frac{1}{s-1}[/tex]
    Y(s) (s+3) - 2 = 8 . [tex]\frac{1}{s-1}[/tex]

    I think the next step is
    Y(s) = [tex]\frac{2}{s+3}[/tex] + [tex]\frac{8}{s-1}[/tex]

    and then do partial fractions but i dont think it leads me to where I need to be. I think i need to make it into a heaviside ??

    Any help would be great. thanks
  2. jcsd
  3. Jan 18, 2008 #2
    After the second step you should get Y(s)= 8/((s-1)*(s+3)) + 2/(s+3)

    After doing a partial fraction expansion you get Y(s)= 4/(s-1)

    which should give you y(t)= ? (I think you can figure it out from here.)
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