we consider the Cauchy problem for a linearly singularly perturbed ordinary

first-order differential equationFor the mentioned reasons, the consideration has been limited to the analysis of the LTV systems described by the

first-order differential equation in the following form:

Chanturiya, "Oscillating and monotone solutions of

first-order differential equations with deviating argument," Differentsial'nye Uravneniya, vol.

This edition, revised from the 2009 seventh, includes eight new projects, updated exercise sets, additional examples and figures, a simplified account of linear

first-order differential equations, new sections on Green's function and the review of power series, and several boundary-value problems involving modified Bessel functions.

He also addresses systems of

first-order differential equations and linear systems with constant coefficients that arise in physical systems, such as coupled spring-mass systems, pendulum systems, the path of an electron, and mixture problems, ending with techniques for determining the behavior of solutions to systems of

first-order differential equations without first finding the solutions.

Second-order differential equation of moving shaft is converted to two sets of

first-order differential equations and solved numerically by MATLAB built-in routine ode45 based on Runge-Kutta method.

The author has organized the main body of his text in five chapters devoted to

first-order differential equations, mathematical models, linear DES of higher order, systems of linear DES, and Laplace transforms.

O'Regan, "Anti-periodic solutions for fully nonlinear

first-order differential equations," Mathematical and Computer Modelling, vol.

The topics are

first-order differential equations, higher-order linear equations, applications of higher-order equations, systems of linear differential equations, the Laplace transform, series solutions, and systems of non-linear differential equations.

Special multi-step methods based on numerical integration such as Adams- Bashforth methods, Adams-Moulton methods and methods based on numerical differentiation for solving

first-order differential equations have been derived in Henrici [3] and Gear [1].

After a review of functions, coverage progresses from limit of a function through derivatives and applications, integrals and applications, techniques of integration,

first-order differential equations, sequences and series, and conics and polar coordinates.

Opening with and overview of discrete dynamical modeling in MATLAB, we proceed into more specific areas, organized by the mathematical foundations: modeling with

first-order differential equations, with matrices, and with both linear and non-linear systems of difference equations.