Estimate of the Measure of Level Set for the Solutions of Differential Equations with Constant Coefficients

We establish the upper estimate of the measure of level set for the functions obtained as solutions of inhomogeneous ordinary differential equations with constant coefficients and right-hand sides without zeros in a certain interval. These estimates can be used for the investigation of entire and meromorphic functions, to study the problem of small denominators for partial differential equations, in the metric theory of Diophantine approximations, and in the theory of measure and integral.