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

Abstract

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.