Most computer codes for solving IVPs accept problems in the form (10). However, problems often arise in different forms. For example, one is often interested in solving the second order equation,

with initial conditions , . Here there is
one unknown function from which we can, * in principle*, obtain
. A new problem can be formed that involves two unknown
quantities, and , but which is in the form (10).
The
idea is to identify * independently* by and
by . Some manipulation then shows that
and satisfy the system,

with