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Example 2.1 - Solve
using the UC method
Example 2.2 - Solve Example 2.1 again using the VOP method
Example 2.3 - Solve 
by simplification using ONMathematical Methods (10/24.539)
II. Linear Differential Equations
Introduction
Many systems can be represented in mathematical form using
Linear Differential Equations. This subject is the main focus of most introductory courses in Differential Equations. In addition, linear ODEs with constant coefficients can be solved using relatively simple analytical approaches, and the characteristic solutions that are obtained are simple elementary functions (sinusoids, exponentials, etc.) and they give significant insight into the physical behavior of the systems under study. Also, much of the mathematical notation (i.e. linear independence, homogeneous, particular, general, and unique solutions, etc.) associated with all differential equations can be introduced concisely and logically through the discussion of linear ODEs. Thus, this is an important subject that warrants a brief review here.In particular, this section overviews the key terminology and analytical procedures needed to solve linear ODEs (of second and higher order). This material is broken into a number of subsections, as follows:
using the UC method
Example 2.2 - Solve Example 2.1 again using the VOP method
Example 2.3 - Solve by simplification using ONThe reader should also see Appendix II for additional modeling and simulation examples involving linear ODEs.
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10/24.539 Lecture Notes by Dr. J. R. White, UMass-Lowell (updated August 1998).
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