标题： 李系统在耗散Milne--Pinney方程中的应用 显示英文标题

标题： Applications of Lie systems in dissipative Milne--Pinney equations

摘要： 我们使用微分方程李系统理论的几何方法来研究耗散埃里马科夫系统。 我们证明了这类方程的解存在叠加规则。 这一事实使我们能够用二阶线性微分方程组的特解和一组常数来表示耗散米尔斯-皮尼方程的通解。 显示英文摘要

摘要： We use the geometric approach to the theory of Lie systems of differential equations in order to study dissipative Ermakov systems. We prove that there is a superposition rule for solutions of such equations. This fact enables us to express the general solution of a dissipative Milne--Pinney equation in terms of particular solutions of a system of second-order linear differential equations and a set of constants.