  We are concerned with the asymptotics and perturbation analysis of a singular
second-order nonlinear ODE that models capillary rise of a fluid inside a
narrow vertical tube. We prove the convergence of the exact solution to a
unperturbed solution when a nondimensional parameter decrease to zero.
Furthermore, we provide an accurate method of approximating the asymptotic
solution for large times. Due to the a fact that the nonlinear component in the
main equation does not satisfy the Lipschitz continuity condition the methods
used to prove the main theorems are nonstandard, require careful analysis, and
can be useful in dealing with similar nonlinear ODEs.
