ABSTRACT
Listed below are simple examples of first-order ordinary differential equations and their solutions having movable singularities:
Equation Solution Solution’s singularity type y′z = –y
2 y = 1/(z – z0) movable pole y′z = 1/y y = 2
√ z – z0 algebraic branch point
y′z = e –y y = ln(z – z0) logarithmic branch point
y′z = –y ln2 y y = exp[1/(z – z0)] essential singularity
Algebraic branch points, logarithmic branch points, and essential singularities are called movable critical points.
