Some integrable nonautonomous dynamical systems with dissipation

In this paper, we search for new examples of integrable second order, complex, linear, nonautonomous, ordinary differential equations. We use the method of canonical transformations, in which the general solution can be expressed in quadratures by means of an explicit generating function. For some types of equations, we show that the general solution can be constructed as an absolutely and uniformly convergent series of a complex parameter that runs through the whole complex plane, while the real-valued independent variable runs through an arbitrarily large segment of the real axis.