$$\frac{dA}{dt} = \iota\beta_1 A + \iota [\gamma_1 + \gamma_2\sin(\Omega t) + \iota\gamma_3\sin(\Omega t + \phi]) B$$
$$\frac{dB}{dt} = \iota\beta_2 B + \iota [\gamma_1 + \gamma_2\sin(\Omega t) + \iota\gamma_3\sin(\Omega t + \phi)] A$$
I can assume a Fourier series for $A$ and $B$ to solve the equations but I was looking for a more robust method to do it. Even if you can point me to relevant literature, that would be grateful. $\beta_1$ and $\beta_2$ and $\gamma$s are constants.
