Abstract
Linear differential equations of higher order have useful and interesting applications, just as first-order differential equations do. We study linear differential equations of higher order in this chapter. The word linear in the chapter title should suggest that techniques for solving linear equations will be important. What is somewhat unexpected is that we have to appeal to the theory of solving polynomial equations in one variable. Though the solution technique for first-order equations gave us a complete solution in essentially one step, this is not the case here. For the first time we have to solve the homogeneous and nonhomogeneous equations separately and by different methods.
Keywords
- Characteristic Polynomial
- Constant Coefficient
- Linear Differential Equation
- Independent Solution
- Linear Differential Operator
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media New York
About this chapter
Cite this chapter
Ross, C.C. (2004). Higher-Order Linear Differential Equations. In: Differential Equations. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3949-7_5
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3949-7_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1941-0
Online ISBN: 978-1-4757-3949-7
eBook Packages: Springer Book Archive