How to solve delay differential equation

[iVenky]

Is there some systematic procedure to solve delay differential equation ?

Here's one equation that I would like to solve

$\large \frac{1}{ \omega } \frac{dV_0(t)}{dt} = V_i(t) - \frac{V_o(t-T_d)}{k}$

where
T_d is the delay

Thanks

 

[pasmith]

Is there some systematic procedure to solve delay differential equation ?

Here's one equation that I would like to solve

$\large \frac{1}{ \omega } \frac{dV_0(t)}{dt} = V_i(t) - \frac{V_o(t-T_d)}{k}$

where
T_d is the delay

Thanks

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