Abstract
Chapter 3 is devoted to analytical methods for the solution of scalar second-order differential equations. Subsequent to the introduction of higher-order equations, solution methods for homogeneous differential equations are presented. This includes, among others, the method of order reduction, solution techniques for exact and pseudo-exact equations, and methods for equations with constant coefficients. Then, solution methods for inhomogeneous equations are presented. Special attention is paid to the method of undetermined coefficients, the method of variation of parameters, and the method of operators.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Coddington, E.A., Levinson, N.: Theory of Ordinary Differential Equations. MacGraw-Hill, New York (1984)
Hartman, P.: Ordinary Differential Equations. Birkhäuser Verlag, Boston/Basel/Stuttgart (1982)
Hermann, M.: Numerische Mathematik, 3rd edn. Oldenbourg Verlag, München (2011)
Saravi, M.: A procedure for solving some second-order differential equations. Appl. Math. Lett. 25(3), 408–411 (2012)
Saravi, M., Hermann, M., Kaiser, D.: Solution of Bratu’s equation by He’s variational iteration method. Am. J. Comput. Appl. Math. 3(1), 4–48 (2013)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer India
About this chapter
Cite this chapter
Hermann, M., Saravi, M. (2014). Second-Order Differential Equations. In: A First Course in Ordinary Differential Equations. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1835-7_3
Download citation
DOI: https://doi.org/10.1007/978-81-322-1835-7_3
Published:
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-1834-0
Online ISBN: 978-81-322-1835-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)