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The Solution of Non-Homogeneous Systems of Differential Equations by Undetermined Coefficients
Published online by Cambridge University Press: 20 November 2018
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The solution of a linear non-homogeneous differential equation whose non-homogeneous term is of the form tkeαt can be obtained by what is usually called the method of undetermined coefficients. The application of this method may be justified in several different ways (see for example [1, pp. 114–117], [2, pp. 94–99], [3]).
We shall consider the analogous problem for a system of differential equations. It turns out that we can solve this problem using only elementary techniques of linear algebra. The solution has essentially the same form as in the case of a single equation, but may contain terms which would not be expected and may lack terms which would be expected in a straightforward extension of the theory to systems. Our method of obtaining the solution is constructive, in the sense that while our results give only the form of the solution, the solution itself may be found by substitution of this form into the system of differential equations.
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- Research Article
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- Copyright © Canadian Mathematical Society 1966
References
1.
Boyce, W. E. and DiPrima, R. C., Elementary Differential Equations and Boundary Value Problems. John Wiley and Sons, New York, (1965).Google Scholar
2.
Coddington, E.A., An Introduction to Ordinary Differential Equations. Prentice-Hall, Englewood Cliffs, N.J., (1961).Google Scholar
3.
Golomb, M., An Algebraic Method in Differential Equations, Am. Math. Monthly, 72, (1965), pages 1107-1110.Google Scholar
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