Multiplicity of an implicit differential equation of degree 3
Abstract
In this paper we introduce the concept of the Multiplicity of an Implicit Differential Equation of Degree 3
F(x,y,p)= a(x,y)p3 + b(x,y)p2 +c(x,y)p+ d(x,y)=0,
where p=dy/dx e a, b, c, d are real analytic functions at an isolated singular point. We also show that the multiplicity introduced here is an invariant under smooth equivalence (Theorem 3.5) and an algebraic formula can be obtained to calculate it under certain reasonable hypothesis.
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