Analytic synthesis of ordinary linear nonstationary differential equations reducible in the sense of Euler
The authors suggest an analytic method for constructing Euler reducible systems. They study the reducibility of an ordinary finite-dimensional \(n\)th-order nonstationary linear differential equation to an equation with constant coefficients. In contrast with the well-known Lyapunov reducibility, which deals with transformations of the state vector and does not affect the independent variable, they consider the Euler reducibility, which deals with the change of the independent variable and does not affect the state vector. They prove that a nonstationary linear (or nonlinear) system is Euler reducible, if there exists a change of the independent variable reducing the system to a system with constant coefficients.
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