I need to classify this PDE into hyperbolic, elipctic or parabolic:
$$C_t+af(t)C_x=-1 \, .$$
Well, once there are not second derivatives, I though in parabolic. However, I understood a professor saying that the Burgers' Equation $u_t+uu_x=0$ is hyperbolic (and it has not second derivatives as well). So, I am confused. Is it so a non-homogeneus hyperbolic PDE?
Many thanks in advance!