Abstract
The movable singularities of solutions of equations of the form y″ = F(z, y)y′ + G(z, y) are studied, where F and G are polynomials in y. It is shown that if degyG ≤ degyF+1 and a certain resonance condition is satisfied, then any movable singularity of y that can be reached by analytic continuation along a finite length curve is algebraic. The case in which degyG ≤ degyF−1 and the only explicit dependence on z in the equation is in the y-independent term of G(z,y) was considered by R. Smith. The movable algebraic and non-algebraic singularities in a particular class of equations of Lienard type satisfying the “maximum balance” condition degyG = 2degyF+1 are also analyzed.
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