Some properties of solutions of second-order linear ordinary differential equations

The Riccati equation method is used to obtain lower and upper estimates for the distance between two consecutive zeros of a solution and the derivative of the solution to a second-order linear ordinary differential equation in terms of its coefficients. Oscillation conditions and a stability condition are proved, and a theorem on the asymptotic behavior of zeros of solutions to a second-order linear equation and on the asymptotic behavior of one of the solutions to this equation is established.