  A subroutine for very-high-precision numerical solution of a class of
ordinary differential equations is provided. For given evaluation point and
equation parameters the memory requirement scales linearly with precision $P$,
and the number of algebraic operations scales roughly linearly with $P$ when
$P$ becomes sufficiently large. We discuss results from extensive tests of the
code, and how one for a given evaluation point and equation parameters may
estimate precision loss and computing time in advance.
