Solutions of ODEs with Removable Singularities

Abstract

We discuss explicit ODEs of the form ẋ = R(t, x), where R is a polynomial or rational function, and the solution x(t) has a removable singularity. We are particularly interested in functions built from elementary functions, such as x(t) = t/ sin t. We also consider implicit ODEs of the forms P (t, x, ẋ) = 0 and P (t, x, ẋ, ẍ) = 0.