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Note on the Peano-Baker Method of solving Linear Differential Equations

Published online by Cambridge University Press:  20 January 2009

Arch Milne
Arch Milne
Affiliation:
Research Student, Edinburgh University Mathematical Laboratory.
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In Mathematische Annalen, Vol. 32 (1888) Peano discusses the solution of a system of homogeneous linear differential equations

where rij denotes a real function of the variable t, and shows how, by a series of repeated substitutions, this system of equations may be replaced by the equivalent equation

where X denotes the complex [x1, x2, … xn] and R the matrix

of which equation the solution X can be represented as a sum of integrals.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , February 1915 , pp. 41 - 44
Copyright
Copyright © Edinburgh Mathematical Society 1916