What is wrong?Help with converting to matlab

> restart; with(PDEtools); > i(t) := -a*v(t)+b*v(t)^3 ; i[D] := i[S]+i(t);

                  i:= t -> -a v(t) + b v(t)^3

                  i[D] :=  i[S] - a v(t) + b v(t)

> eq[1] := i[C]+i[D]+i[R]-i[L](t) = 0;

      eq1:=i[C] + i[S] - a v(t) + b v(t)  + i[R] - i[L](t) = 0

> V[D] := V[S]+v(t); V[C] := V[D]; V[R] := V[D]; V[D]:=V[S] + v(t) V[C}:=V[S] + v(t) V[R]:=V[S] + v(t) >i[C] := C*(diff(V[C], t)); i[R] := V[R]/R;

                            / d      \
                     i[C]:= |--- v(t)|
                            \ dt     /

                      i[R]:= V[S] + v(t)
                             -----------
                                 R     
>eq[1];

/ d      \                         3   V[S] + v(t)              
C |--- v(t)| + i[S] - a v(t) + b v(t)  + ----------- - i[L](t) = 0
\ dt     /                                  R                   
>eq[2] := diff(eq[1], t);
    / d  / d      \\     / d      \           2 / d      \
eq2:=C |--- |--- v(t)|| - a |--- v(t)| + 3 b v(t)  |--- v(t)|
    \ dt \ dt     //     \ dt     /             \ dt     /

          d                          
         --- v(t)                    
          dt        / d         \    
       + -------- - |--- i[L](t)| = 0
            R       \ dt        /

>V[L] := V[S]-V[D];V[b]=V[D] V[L]:= -v(t)

>de := subs(diff(i[L](t), t) = V[L]/L, eq[2]); / d / d \\ / d \ 2 / d \ C --- |--- v(t)| - a --- v(t) + 3 b v(t) --- v(t) \ dt \ dt // \ dt / \ dt /

          d                 
         --- v(t)           
          dt        v(t)    
       + -------- + ---- = 0
            R        L

>expand(de/C); / d \ 2 / d \ d a --- v(t) 3 b v(t) --- v(t) --- v(t) / d^2 \ \ dt / \ dt / dt --- v(t) - ------------ + -------------------- + -------- \ dr^2 / C C C R

     v(t)    
   + ---- = 0

     C L     
>collect(%, diff(v(t), t));

/ 2 \ 1 a 3 b v(t) | / d \ / v(t) / d^2 \\ |-- - - + --------- |* -- v(t) + | --- + | --- v(t)|| *v(t) = 0 \CR C C / \ dt / \ CL \ dt^2 //

>de[2] := subs(v(t)/(C*L) = w^2*v(t), %); / 2 \ | a 3 b v(t) 1 | / d \ / d ^2 \ de2:= - - + --------- + ---* --- v(t) + w^2 v(t)+ ------- v(t) = 0 \ C C C R/ \ dt / \ dt^2 /

               2

>tr := {t = tau/w, v(t) = x(tau)*sqrt(a-1/R)/sqrt(3*b)};

                                                            \
         /                                      
         |                         /    \            1     
         |                         x(tau  sqrt (|a - -|sqrt(3))     
  tr:=         tau          1      \    /            R      
         |t = -----, v(t) = -      ---------------------- 
         |    omega         3        sqrt  (3*b)           
         \                                                  /

>sqrt(3*b)*dchange(tr, de[2], [x(tau), tau], simplify)/(omega^2*sqrt(a-1/R));

expand(%); / d \ x(tau) ----- x(tau) a \ dtau / / d / d \\ ------------------------ + x(tau) + ----- |----- x(tau)| omega C R \ dtau \ dtau //

           2 /  d         \   /  d         \       d             
     x(tau)  |----- x(tau)|   |----- x(tau)| a   ----- x(tau)    
             \ dtau       /   \ dtau       /      dtau           
   - ---------------------- - ---------------- + ------------ = 0
           omega C R              omega C         omega C R

>collect(%, diff(x(tau), tau), factor);

                                      /  d         \         
  (x(tau) - 1) (x(tau) + 1) (R a - 1) |----- x(tau)|         
                                      \ dtau       /         
  -------------------------------------------------- + x(tau)
                      omega C R                              

       /  d   /  d         \\    
     + |----- |----- x(tau)|| = 0
       \ dtau \ dtau       //

>de[3] := subs(x(tau)-1 = -(1-x(tau)^2)/(x(tau)+1), %); / 2\ / d \ \1 - x(tau) / (R a - 1) ----- x(tau) \ dtau / - -------------------------------------- + x(tau) omega C R

            /  d   /  d         \\    
          + |----- |----- x(tau)|| = 0
            \ dtau \ dtau       //

>subs(R*a-1 = epsilon*omega*C*R, %); / 2\ / d \ -\1 - x(tau) / epsilon ----- x(tau) + x(tau) \ dtau /

              /  d   /  d         \\    
            + |----- |----- x(tau)|| = 0
              \ dtau \ dtau       //

provided that epsilon is positive. Since a,w(omega),and C are positive, this condition requires that the resistance R>1/a.

[Rik]

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