A total of \(n\) machines are connected to an electric transmission line. The probability that a machine consuming power at time \(t\) will cease to consume up to time \(t+\Delta t\) is equal to \(\alpha \Delta t+o(\Delta t)\). If at time \(t\) a machine is not consuming any power, then the probability that it will begin consuming prior to time \(t+\Delta t\) is equal to \(\beta \Delta t+o(\Delta t)\), irrespective of the operation of the other machines. Form differential equations that are satisfied by the probabilities \(P_{r}(t)\) that at time \(t\) a total of \(r\) machines will be consuming power.

It is easy to indicate the concrete conditions of this problem: the movement of trams, electric welding, power consumption by machine tools with automatic cutoff, and so forth.