  The answers for Feynman diagrams satisfy various kinds of differential
equations -- which is not a surprise, because they are defined as Gaussian
correlators, possessing a vast variety of Ward identities and
superintegrability properties. We study these equations in the simplest example
of banana diagrams. They contain any number of loops, but can be efficiently
handled in position rather than momentum representation, where loop integrals
do not show up. We derive equations for the case of scalar fields, explain
their origins and drastic simplification at coincident masses. To further
simplify the story we do not consider coincident points, i.e. ignore
delta-function contributions and ultraviolet divergences for the most part. The
equations in this case reduce to homogeneous and have as many solutions as
there are different Green functions -- $2^n$ for $n$ loops in quadratic theory,
what reduces to just $n+1$ for coincident masses, i.e. for a single field. We
comment on the recovery of the delta-functions directly from the homogeneous
equations and also compare our result with momentum space formulas known in the
literature.
