LaplaceTransform works well with x[t], but doesn't recognize x[1][t], how to make it works for x[1][t]?

Question

Bug introduced in 12.2(?), persisting through 14.0 or later.

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When I am solving odes using LaplaceTransform, I found that LaplaceTransform works well with u[t] or y[t] or x[t], but doesn't recognize x[1][t].

So, how to make LaplaceTransform know x[1][t]?

Thanks.

In[125]:= LaplaceTransform[a x[t] + b y'[t], t, s] // Simplify
Out[125]= 
a LaplaceTransform[x[t], t, s] + b s LaplaceTransform[y[t], t, s] - 
 b y[0]
In[126]:= LaplaceTransform[a x[1][t] + b x[2]'[t], t, s] // Simplify
Out[126]= LaplaceTransform[a x[1][t] + b Derivative[1][x[2]][t], t, s]

Answer 1

Obviously a bug. (If I guess it right, it's introduced in v12.2 together with this bug. ) v9.0.1 gives the desired result:

A possible fix is turning to the method mentioned here:

Unprotect@LaplaceTransform;
LaplaceTransform[(h : Plus)[a__], t_, w_] := LaplaceTransform[#, t, w] & /@ h[a]
Protect@LaplaceTransform;