Differential equations of the form y′=f(t,y,y′), where f is not
necessarily linear in its arguments, represent certain physical phenomena and
are known for quite some time. The well known Clairut's and Chrystal's
equations fall into this category. Earlier, we established the existence of a
(unique) solution of the nonstandard initial value problem (NSTD IV P)
y′=f(t,y,y′), y(t0)=y0 under certain natural hypotheses on f. In this paper
we present some first order convergent numerical methods for finding the
approximate solutions of the NST D I V Ps.