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The motions of algebraic differential equations

Published online by Cambridge University Press:  18 May 2009

Lee A. Rubel
Lee A. Rubel
Affiliation:
Department Of Mathematics, University Of Illinois, Urbana Illinois 61801, U.S.A.
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We confine ourselves, for simplicity, to first-order algebraic differential equations (ADE's), although analogous considerations may be made for higher-order ADE's:

P(x, y(x), y'(x)) = 0. (*)

A motion of (*) is a change of independent variable that takes solutions to solutions, that is, a suitable map <p of the underlying interval I into itself so that if y is a solution of (*) then y ° φ is a solution of (*), i.e.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 1 , January 1984 , pp. 93 - 96
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

REFERENCES

1.Burnside, W. S. and Panton, A. W., Theory of equations (Dublin, 1904). (Also Dover reprint.)Google Scholar
2.Ritt, J. F., Integration in finite terms (Columbia U. P., 1948).CrossRefGoogle Scholar