Question:dchange pde maple

Question:dchange pde maple

Dear all,

I have a problem with dchange ....  use the dchange command to transform pde to the
x[1], x[2].

> restart;
> with(PDEtools); with(LinearAlgebra);
> pde := diff(u(t), t, t)+2*GAMMA*(diff(u(t), t))+omega^2*u(t) = 0;
/ d  / d      \\           / d      \        2
|--- |--- u(t)|| + 2 GAMMA |--- u(t)| + omega  u(t) = 0
\ dt \ dt     //           \ dt     /
> deq1 := diff(u(t), t) = v(t);
d
--- u(t) = v(t)
dt
>
> deq2 := subs(deq1, pde);
/ d      \                       2
|--- v(t)| + 2 GAMMA v(t) + omega  u(t) = 0
\ dt     /
>
> dsolve({deq1, deq2}, {u(t), v(t)});
>
> eqns := [rhs(deq1) = lhs(deq1), rhs(deq2) = lhs(deq2)];
[        d            / d      \                       2     ]
[v(t) = --- u(t), 0 = |--- v(t)| + 2 GAMMA v(t) + omega  u(t)]
[        dt           \ dt     /                             ]
> y := [u, v]; b := diff(y(t), t);
[u, v]
[ d         d      ]
[--- u(t), --- v(t)]
[ dt        dt     ]
> A, b := GenerateMatrix(eqns, y(t));
Matrix(%id = 122038892), Vector[column](%id = 135944696)
# Return a vector of eigenvalue of A and matrix  whose columns are eigenvectors of A
> gnat := Eigenvectors(A);
> lambda := gnat[1]; Lambda := gnat[2];
Vector[column](%id = 135975976)
Matrix(%id = 136787860)
> Y := Vector([y]);
Vector[column](%id = 123771808)
> tr := solve(GenerateEquations(Lambda, [x[1], x[2]], Y), {u, v});
/           /                                    (1/2)
|      1    |                   /     2        2\
< u = ------ \-x[1] GAMMA - x[1] \GAMMA  - omega /      - x[2] GAMMA
|         2
\    omega

(1/2)\                 \
/     2        2\     |                 |
+ x[2] \GAMMA  - omega /     /, v = x[1] + x[2] >
|
/
>
> dchange(tr, pde, [x[1], x[2]]);

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