engleski

On parameter classes of solutions of second order linear differential equation

This paper studies a second order linear differential equation transforming it to a corresponding system of linear equations. We consider the solutions of that system with respect to a corresponding "square" neighbourhood of an integral curve. We establish the behaviour of certain classes of Cauch's solutions depending on two, one or zero parameters for corresponding sufficient conditions. The results thus obtained refer also to the problem of stability of solutions. Some of the results can be directly applied to a quasi-linear equation.

Second order linear differential equation; parameter classes of solutions; stability of solutions

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