Fundamental Solution of an Implicit Linear Inhomogeneous First Order Differential Equation Over an Arbitrary Ring

We study the simplest implicit linear inhomogeneous differential equation of the first order by_ + R(x) = y over an arbitrary commutative ring. It is shown that the Euler series can be regarded as the fundamental solution to such an equation in the ring of formal Laurent series with finitely many po...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2016-12, Vol.219 (6), p.922-935
Main Authors: Gefter, S. L., Goncharuk, A. B.
Format: Article
Language:English
Subjects:
Backup software
Commutativity
Differential equations
Mathematics
Mathematics and Statistics
Polynomials
Rings (mathematics)
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Summary:We study the simplest implicit linear inhomogeneous differential equation of the first order by_ + R(x) = y over an arbitrary commutative ring. It is shown that the Euler series can be regarded as the fundamental solution to such an equation in the ring of formal Laurent series with finitely many positive degrees and in the ring of Laurent polynomials. Bibliography: 9 titles.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-016-3155-9