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The method of Riccati’s equation is applied to find a stability criterion for systems of two first-order linear ordinary differential equations. The obtained result is compared for a particular example with results obtained by the Lyapunov and Bogdanov methods, by using estimates of solutions of systems in terms of the Losinskii logarithmic norms, and by the freezing method.
Based on two comparison theorems we obtain some coefficient characteristics of global solvability of scalar Riccati equations. The results are applied to investigation of a system of two linear first-order differential equations.
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