#nonlinearordinarydifferentialequations — Public Fediverse posts

(He attributes the proof of that to Painlevé)

Does that still apply if the "first-order equation" is actually an nth-order equation that has been made first-order by the old trick of writing the dependent variable and its first n-1 derivatives as components of a vector-valued function?

2/2

#mathematics #ordinaryDifferentialEquations #nonLinearOrdinaryDifferentialEquations

Any mathematicians out there? A question:

Hille (1969, _Lectures on Ordinary Differential Equations_, Addison-Wesley) says, if a first-order (nonlinear) ordinary differential equation sets the derivative of the dependent variable to a function of the dependent variable and the independent variable that is rational in the dependent variable, then all movable singularities of the solution must be algebraic 1/2

#mathematics #ordinaryDifferentialEquations #nonLinearOrdinaryDifferentialEquations