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Example 1:
f'(t, f, g, h) = g
g'(t, f, g, h) = h
h'(t, f, g, h) = -t h + 3t g + 2f + t
The example 1 of NSolveODE command represent this ODE equation:
y'''+t*y''- 3*t*y '+ 2*y - t = 0
Example 2:
x1'(t, x1, x2, x3, x4) = x2
x2'(t, x1, x2, x3, x4) = x3
x3'(t, x1, x2, x3, x4) = x4
x4'(t, x1, x2, x3, x4) = -8x1 + sin(t) x2 - 3x3 + t^2
The example 2 of NSolveODE command represent this ODE equation:
y''''+3*y'''- sin(t)*y'+8*y'-t^2=0
The same question 
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