Question: Need help for substitution in pde!

I am doing some solution for pde :

restart;
with(PDEtools);
with(plots);
alias(u = u(x, y, t), w = w(x, y, t), f = f(w));
pde := diff(u, x, x, x, y) + 3*diff(u, y)*diff(u, x, x) + 3*diff(u, x)*diff(u, x, y) + 2*diff(u, y, t) = 0;
pde2 := subs(u = D(f)(w)*diff(w, x) + u0(x, y, t), pde);

pde3 := expand(pde2);


after this step i want to substitute 
D(f)(w)*D^(3)(f)(w)= (-c/3)*D^(4)(f)(w)

so i apllied command as this :

pde33 := subs({D(f)(w)*(D^(3)(f)(w) = -c/3*(D^(4)(f)(w)}, pde3);

but i not able to replace it !

please help in it ! Thanks!


 

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