the following integral equation must be solved for x(t). $$x(t) + \mu(t) \frac{1}{T} \int_{T}x(\tau)h(t-\tau)d\tau = y(t)$$
where $y(t)$, $\mu(t)$, and $h(t)$ are all known functions. All functions are periodic with period $T$. $y(t)$ and $mu(t)$ are rectangular-shaped while $h(t)$ is something complicated.
is there an analytic solution which gives the answer with great precision? I once attempted to solve with fourier series, and since I could use only a few number of harmonics, the solution was not perfectly precise.
if there is a solution using laplace transform in piecewise mode, or other analytic methods, would be appreciated.