Geodesic
An Elementary Proof of the Frobenius Factorization Theorem for Differential Equations
Canadian mathematical bulletin, Tome 17 (1974) no. 3, pp. 379-380

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Consider the 1st order linear system 1 when An(t) is real valued and continuous on I, a i, i+1(t) ≠ 0, aij (t) ≡ 0 for j ≥ i + 2, t ∊ I and i = 1, ..., n — l. In what follows, components cj of a vector c will be identifiable by the superscript. The purpose of this note is to give a simple induction proof of the following theorem of Frobenius [1]. 
Kennedy, E. W. An Elementary Proof of the Frobenius Factorization Theorem for Differential Equations. Canadian mathematical bulletin, Tome 17 (1974) no. 3, pp. 379-380. doi: 10.4153/CMB-1974-069-7
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     author = {Kennedy, E. W.},
     title = {An {Elementary} {Proof} of the {Frobenius} {Factorization} {Theorem} for {Differential} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {379--380},
     year = {1974},
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     number = {3},
     doi = {10.4153/CMB-1974-069-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-069-7/}
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