we consider the Cauchy problem for a linearly singularly perturbed ordinary first-order differential equation
For 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  and Gear .
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.