# 11.2  Direction Fields
# Art Belmonte, Summer 1996
# These are the shaded gray examples which appear in Section 11.2. 
# 
# NOTE! The DEtools package has been rewritten and expanded for Maple V
# Release 4. To find out more, select Help -> Contents -> What's New ->
# Symbolics -> DEtools.
# 
> restart; with(DEtools);

[DEnormal, DEplot, DEplot3d, Dchangevar, PDEchangecoords, PDEplot,

    autonomous, convertAlg, convertsys, dfieldplot, indicialeq,

    phaseportrait, reduceOrder, regularsp, translate, untranslate,

    varparam]

# One thing which has changed in Release 4 is the syntax of the
# dfieldplot command. For details, type ?dfieldplot at a Maple prompt.
> dfieldplot(diff(y(x), x) = x*sin(y(x)), y(x), x=-2..2, y=-1..1);
# Here is way (different from that originally given in CalcLabs with
# Maple V) to plot a solution curve on top of the direction field for
# the preceding differential equation. It is preferable for two reasons:
#      1. It uses one command instead of five.
#      2. It works with differential equations for which no explicit
# solution can be found.
> DEplot({diff(y(x), x) = x*sin(y(x))}, {y(x)},
>      x=-2..2, [[y(0)=1/4]], y=-1..1);
>