Geodesic
The Peano--Baker series
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 167-171

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This note reviews the Peano–Baker series and its use to solve the general linear system of ODEs. The account is elementary and self-contained, and is meant as a pedagogic introduction to this approach, which is well known but usually treated as a folklore result or as a purely formal tool. Here, a simple convergence result is given, and two examples illustrate that the series can be used explicitly as well. 
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     author = {Michael Baake and Ulrike Schl\"agel},
     title = {The {Peano--Baker} series},
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}
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Michael Baake; Ulrike Schlägel. The Peano--Baker series. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 167-171. http://geodesic.mathdoc.fr/item/TM_2011_275_a8/