Abstract
The solutions of a homogeneous, linear secondorder difference equation with constant coefficients a and b. C1, C2, and ω are arbitrary constants. If the function c t is itself a solution of the homogeneous equation, multiply the trial solution by t. If this new trial function also satisfies the homogeneous equation, multiply the trial function by t again. (See Hildebrand (1968), Sec. 1.8 for the general procedure.)
Keywords
- Equilibrium State
- Linear System
- Periodic Solution
- Difference Equation
- Arbitrary Constant
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References
Most of the formulas and results are found in e.g. Goldberg (1961), Gandolfo (1996), and Hildebrand (1968). For (10.19) and (10.20), see Farebrother (1973). For (10.29)–(10.36), see Sydsæter et al. (2005).
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© 2010 Springer-Verlag Berlin Heidelberg
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Sydsæter, K., Strøm, A., Berck, P. (2010). Difference equations. In: Economists’ Mathematical Manual. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28518-2_10
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DOI: https://doi.org/10.1007/978-3-540-28518-2_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26088-2
Online ISBN: 978-3-540-28518-2
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