Compare the symbolic solution with numerical solution

Questions
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1

I am trying to compare the symbolic solution with numerical solution by using NDSolve. But the two curves are not match when I plot it. Please give me suggestions how to improve the plot?

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2

I don’t understand. The function xIII does not seem to be a solution of eq1:

Simplify[eq1 /. x -> xIII]
3

Sorry “xIII=2 i sec(t)”, then output is true.

4

num = NDSolveValue[
eq1 && (x[0] == xIII[0]) && (x’[0] == xIII’[0]) && (x’‘[0] ==
xIII’'[0]), x, {t, -1, 1}];
ReImPlot[num[t] - xIII[t], {t, -1, 1}]

5

xIII[t_] = 2 I Sec[t];

6

I tried it, but no plot output on my computer.

7

Gianluca’s answer works fine for me. You probably have a conflicting prior definition for some symbol(s). Try with a fresh kernel or evaluate the following prior to evaluating the rest of the code.

ClearAll[Evaluate[Context[] <> "*"]]
8

still no output plot. I got just one result i.e.,

mNB_second_case.nb (19.5 KB)

9

You give initial data that do not match xIII:

{xIII[0], xIII'[0], xIII''[0]}
With[{ww = 10^(-2), tt = 1},
  {x0 = xA /. w -> ww,
   x0p = Sqrt[ww - x0^2 - (1/4) x0^4],
   x00p = -x0 - (1/2) x0^3}] // N

How can you expect the solutions to coincide?