When x1(t)=sin(t) - no problem.
When x1(t) is my function - an error!
See please the attach.
Three-Planets (Mathcad Block).sm (38 KiB) downloaded 61 time(s).

This is because the solution functions are defined using interpolation. The interpolation functions have the X and Y vectors and the value of x as arguments. You try to provide a vector for x. Vectorize can handle only matrix arguments of the same size and successively calls the function with the j-th element of each vector.

So vectorize would require your x vector to be of the same size as the data vectors. Even in this case this probably will fail because the data would be reduced to a single X_i and Y_i.

Therefore, you have to use a loop.

Vectorize works fine in this document.

Three-Planets.sm (41 KiB) downloaded 60 time(s).

Wrote

Vectorize works fine in this document.

Three-Planets.sm (41 KiB) downloaded 60 time(s).

Sorry - no. See please the attach
Three-Planets.sm (39 KiB) downloaded 70 time(s).

Wrote

Sorry - no. See please the attach

As I open your returned document,
both vectorize are red ... click on either one ... Bingo