' - - File:XIVd  ' 2nd Order differential equation.

'G{t,x,y} =  y + 2x
'F{t,x,y} =   y +    x
' This system is converted to   X''(t)  -  2x(t)  -  x(t) = 0  for checking.
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F{t,x,y} = y                                           '     Solution checks with exact value to within 1E-4
G{t,x,y} = 2y + x                               
                                                                  a = 1 + Sqrt[2]  :   b = 1 - Sqrt[2]
                                                                  X{t} =  2*Exp[a*t] + 2*Exp[b*t]
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to = 0 : tf =2 :   xo = 4  :  yo = 4

IVP[F,G,{to,tf,xo,yo}{1 , 0.05,1}]

' Remove the comments (') from the top system and comment out the lower F,G system.
' The result are the same when plotted.

' NOTE: If a  msg indicated 1000 points reached.-- decrease TOL or increase FACTOR.
' Still look at the partial plot if you wish.

A<t> = <t, X, 0>
Plot[A, {t, to, tf, 50}]


