' - - File: VIII_Multi6.txt

' Given F{x,y}:
'   1.  Plot the slope field & the particular soutions defined. Plot.
'   2.  Comment out PlotSlopeField & remove comment from Plot command.
'   3.  Plot the exact solutions based upon the two initial conditions.
'   4.  If you wish, combined both on one plot sheet.

' Given (x,y) --> <F, H>, construct the directed field. Try  h = 0.05 setting.

F{x,y} = y - x

a = -2  :  b =6  :  n = 9
c = -2  :  d = 6:  m = 9

x1 = 0  :  y1 =2/3
x2 = 0  :  y2 = 2
PlotSlopeField[F, {a,b,n}{c,d,m}{x1,y1}{x2,y2}]

Ga{x} = x + 1 - 1/3 * Exp[x]  :  Pa<x> = <x, Ga{x},0>     ' First particular solution.
Gb{x} = x + 1 + Exp[x]          :  Pb<x> = <x, Gb,0>         ' Second particular solution.
Plot[Pa, Pb, {x,0,3 ,100}]




