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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