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How to solve delay differential equation

  1. Nov 6, 2013 #1
    Is there some systematic procedure to solve delay differential equation ?

    Here's one equation that I would like to solve

    [itex] \large \frac{1}{ \omega } \frac{dV_0(t)}{dt} = V_i(t) - \frac{V_o(t-T_d)}{k} [/itex]

    where
    Td is the delay

    Thanks
     
  2. jcsd
  3. Nov 6, 2013 #2

    pasmith

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    Homework Helper

    The equation is linear, so Laplace transforms are suitable:
    [tex]
    \mathcal{L}[f(t)] = \int_0^\infty e^{-st} f(t)\,dt = F(s)
    [/tex]
    You will need to use
    [tex]
    \mathcal{L}[f(t - t_0)] = e^{-st_0} \int_{-t_0}^0 e^{-su} f(u)\,du + \mathcal{L}[f(t)]
    [/tex]
     
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