The method of approximate solution of a system of differential equations from the Ramsey–Kass–Koopmans model, based on the solution in quadratures of one subclass of similar systems

The article is devoted to the Ramsey–Kass–Koopmans model. We consider an auxiliary system of differential equations, which is analogous to the system that arises in the case of constancy of the stationary rate of savings. We found that systems of this class are solved in quadrature. This allows us to find approximate solutions to the system describing the original model.