  A modification of the spiked harmonic oscillator is studied in the case for
which the perturbation potential contains both an inverse power and a linear
term. It is then possible to evaluate trial functions by solving an integral
equation due to the occurrence of the linear term. The general form of such
integral equation is obtained by using a Green-function method, and adding a
modified Bessel function of second kind which solves an homogeneous problem
with Dirichlet boundary condition at the origin.
