Question: dchange pde maple

Dear all,

I need your help

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]]);