  We derive the analytical solutions to the second order generalised
gravi-proprioceptive equation given in our recent paper [Bastien et al. 2012].
These equations show how plants adjust to the surrounding gravitation field and
highlight the fact that the plant must be able to not only sense its local
posture with respect to the gravitational field, but also to sense its own
local curvature. In [Bastien et al. 2012] we obtained explicit analytical
solutions of these equations in terms of (sums of) Bessel functions, and in the
present paper we derive these solutions.
