Abstract
This chapter focuses on higher-order linear equations. Even for second-order linear equations, no general method of solution is available as there was for first-order equations. Formulas for general solutions can be found for certain special classes of higher-order equations. The chapter describes the important basic properties of solutions of linear differential equations in general. Homogeneous equations are considered for this purpose. A theory for non-homogeneous equations, based on that for homogeneous equations, is described. For the applications that give rise to differential equations, real solutions of the equations are considered. However, sometimes it is convenient to extract a desired real solution from a complex solution. In case the associated homogeneous equation has constant coefficients, or is of the Cauchy-Euler type, it could be solved.
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