The Solution of Non-Homogeneous Systems of Differential Equations by Undetermined Coefficients
Canadian mathematical bulletin, Tome 9 (1966) no. 4, pp. 481-487
Voir la notice de l'article provenant de la source Cambridge
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.
Brauer, Fred. The Solution of Non-Homogeneous Systems of Differential Equations by Undetermined Coefficients. Canadian mathematical bulletin, Tome 9 (1966) no. 4, pp. 481-487. doi: 10.4153/CMB-1966-059-7
@article{10_4153_CMB_1966_059_7,
author = {Brauer, Fred},
title = {The {Solution} of {Non-Homogeneous} {Systems} of {Differential} {Equations} by {Undetermined} {Coefficients}},
journal = {Canadian mathematical bulletin},
pages = {481--487},
year = {1966},
volume = {9},
number = {4},
doi = {10.4153/CMB-1966-059-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-059-7/}
}
TY - JOUR AU - Brauer, Fred TI - The Solution of Non-Homogeneous Systems of Differential Equations by Undetermined Coefficients JO - Canadian mathematical bulletin PY - 1966 SP - 481 EP - 487 VL - 9 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-059-7/ DO - 10.4153/CMB-1966-059-7 ID - 10_4153_CMB_1966_059_7 ER -
%0 Journal Article %A Brauer, Fred %T The Solution of Non-Homogeneous Systems of Differential Equations by Undetermined Coefficients %J Canadian mathematical bulletin %D 1966 %P 481-487 %V 9 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-059-7/ %R 10.4153/CMB-1966-059-7 %F 10_4153_CMB_1966_059_7
Cité par Sources :