# Solve Differential Equation with Laplace Transform

Using Laplace Transforms, I am trying to solve the following differential equation:

$$frac{dB(t)}{dt} = (j (omega_0 – m cos(omega_mt)) – g) B(t) – j A$$

where
$$B(0) = 0$$

Using Laplace Transforms, the differential equations becomes:

$$s B(s) + (g – j omega_0) B(s) + m Laplace( B(t) cos(omega_m t) ) = – j frac{A}{s}$$

I can take the

$$Laplace (B(t) cos(omega_m t))$$

assuming
$$cos(omega_m t) = frac{1}{2} exp(j omega_m t) + frac{1}{2} exp(-j omega_m t)$$

At this point, I am not sure how to solve for B(s)