I tried with numerics with NDSolve
the kernel shutdown looks like a bug on Mathematica 12.2.0
Maybe you can try:
solution =
Block[{Integrate},
DSolve[Rationalize[{DE1 == 0, displacement[0] == 0,
DE2 == 0 /. X1 -> length}, 0],
displacement[X1], {X1, 0, 3/2}] /. {Integrate ->
Inactive[Integrate]}] // Simplify // Activate
but answer is very complicated solution by InverseFunction
and Integral
s.
I don't have time to solve this problem.
Regards M.I.