In this paper, we investigate the first-order differential equation
of the form:
The generalization of Riemann problem to a linear first-order differential equation
together with the linear boundary condition
The first-order differential equation
, from which the trajectories in phase- space, i.
The function q = q([theta]) will then satisfy an ordinary differential equation, which can be integrated twice to result in a first-order differential equation
of the form
The motivation for the work carried out in this paper arises from the methods based on numerical differentiation for the first-order differential equation
, and special multi-step methods based on numerical differentiation for the solution of the special second-order have been derived in Rma Chandra Rao .
The authors cover traditional first-order differential equations
, geometrical and numerical methods for first-order equations, elements of higher-order linear equations, and a wide variety of other related subjects.
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.
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.