In connection with the problem of stability of servo-mechanisms, whose elements vary with time t, stability property of some ordinary differential equation is studied. Firstly, a linear ordinary differential equation, whose coefficients vary with time t, is considered. The variation with time t is regarded to be expressed by linear functions of ξ, where [function]. It is shown that the solution of the given linear differential equation, thus specified, can be expressed as power sesies with respect to ξ, by means of which, the question of stability may be examined. Secondly, it is pointed out that, the problem of similar kind, for the case of non-linear servo-mechanism, can be studied, by following the classical method of É. Picard.