ABSTRACT
Ordinary differential equations (ODEs) may be divided into two classes: linear equations and nonlinear equations. The latter have a richer mathematical structure than linear equations and are generally more difficult to solve in closed form. The text is very selective in presenting general statements about linear n-th order differential equations because it has a different goal. The theorems are usually proved only for second order equations. Second order differential equations are widely used in science and engineering to model real world problems. The method of undetermined coefficients is simple and has important applications, but it is applicable only to constant coefficient equations with a special forcing function. The boundary conditions are imposed on the unknown function on at least two different points. The differential equation with the initial conditions is called the initial value problem or the Cauchy problem.
