A STUDY OF PROPERTIES OF SOLUTIONS OF DIFFERENTIAL EQUATIONS

Abstract

A Study of properties of solutions of Differantial Equations newlineA differantial equation is an equation in mathematics it is unknown for one as well as various variables are related to the values of function and itself as well as its derivatives of various order. Differantial equations originated in Newton s effort to explain the motion of particles and mainly used to describe the change of quantities or behavior of certain systems in applications, such as those governed by Newtonian laws or many other things. The theory of differential equations, the methods used in their solutions and their wise applications have all advanced to the extent that aspects in each of these areas have demanded individual attention. newlineTheory of models given for dynamical system that can be stated space models as well as customary to suppose any external input or output. As well as this is an very well develop theory for passing through an one type of model to another type of model. Therefore in this theory more efficient algorithm for passes from an convolution to function transfer as well as to an state model and back. Also here we having stochastic as well as non-linear system, here availability of so many methods for helping representation of first order state to higher order model. newlineTherefore much understands the interaction from to system variable which is needed in various applications as well as further understanding of behavior of functions given from those variables. Obviously in many conditions such type of functions are crucial in dissipative system theory also in optimal control which is in Lyapunov theory. Such contexts we note that observation of theory gives for dynamics which is nearly invariably concentrate on representation states as well as first order models. Therefore in newlineIV newlinethe study of system stability by the use of Lyapunov method, we suppose that representation of states as well as problems in optimal control invariably consider that the value gives in integral of function of input as well as states. Here an question ar