I need to solve the following Integro-Differential Equation. $$ \begin{equation} \frac{da}{dt} = (-i\Delta-\kappa)a + c -\int_{-\infty}^0 e^{-\gamma(t-\tau)}g(\tau)a(t-\tau)d\tau, \end{equation} $$ in which, $g(\tau)=\alpha e^{-\tau^2/2\sigma}$, $\Delta,\ \kappa,\ c,\ \sigma$ are positive constants. I have tried to Fourier transform the equation but it is still very messy. Could anyone tell me how to solve this equation? Thanks!
2026-02-25 01:55:50.1771984550
How to solve this damped integro-differential equation?
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