  It is well known that second order homogeneous linear ordinary differential
equations with slowly varying coefficients admit slowly varying phase
functions. This observation underlies the Liouville-Green method and many other
techniques for the asymptotic approximation of the solutions of such equations.
It is also the basis of a recently developed numerical algorithm that, in many
cases of interest, runs in time independent of the magnitude of the equation's
coefficients and achieves accuracy on par with that predicted by its condition
number. Here we point out that a large class of second order inhomogeneous
linear ordinary differential equations can be efficiently and accurately solved
by combining phase function methods for second order homogeneous linear
ordinary differential equations with a variant of the adaptive Levin method for
evaluating oscillatory integrals.
