# CANONICAL FORMS AND SOLVABLE SINGULAR SYSTEMS OF DIFFERENTIAL EQUATIONS

@article{Campbell1983CANONICALFA, title={CANONICAL FORMS AND SOLVABLE SINGULAR SYSTEMS OF DIFFERENTIAL EQUATIONS}, author={Stephen L. Campbell and Linda R. Petzold}, journal={Siam Journal on Algebraic and Discrete Methods}, year={1983}, volume={4}, pages={517-521} }

In this paper we investigate the relationship between solvability and the existence of canonical forms for the linear system of differential equations $E ( t ) x' ( t ) + F ( t ) x ( t ) = f ( t )$. We show that if E, F are analytic on the interval $[ 0 \,\, T ]$, then the differential equation is solvable if and only if it can be put into a certain canonical form. We give examples to show that this is not true if E, F are only differentiable.

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