  We show that the gravitational potential in the plane of an axisymmetrical
flat disk where the surface density varies as a power of the radius obeys an
inhomogeneous first-order Ordinary Differential Equation (ODE) solvable by
standard techniques. The potential being exactly known at the origin for any
power index (and at infinity as well), the search for solutions consists of a
Two-point Boundary Value Problem (TBVP) with Dirichlet conditions. The
computating time is then linear with the number of grid points, instead of
quadratic from direct summation methods. Complex mass distributions which can
be decomposed into a mixture of power law surface density profiles are easily
accessible through the superposition principle. This ODE definitively takes the
place of the untractable bidimensional Poisson equation for planar
calculations. It opens new horizons to investigate various aspects related to
self-gravity in astrophysical disks (force calculations, stability analysis,
etc.).
