I have an ODE containing different orders of differentiation of f1(x), f2(x) and f3(x).

> with(PDEtools):

> difforder(ODE);

or

> difforder(ODE,x);

gives the order with respect to x but I need a "COMMAND" doing below,

> ODE:=12*diff(f1(x),x$5)^(7/2)*diff(f2(x),x$4)^9+12*diff(f3(x),x$3)*diff(f1(x),x$2)^9;

> COMMAND (ODE,f1(x));

5

> COMMAND (ODE,f2(x));

4

> COMMAND (ODE,f3(x));

3

I have a differential equation, let us call it

F:=12*diff(u(x),x$7)^(3/2)*diff(u(x),x$2)^3+8*diff(u(x),x$6)^4+4*diff(u(x),x$4)*diff(u(x),x$3);

First, I need to know the term containing the highest order derivative:

with(PDEtools):

k:=difforder(F);

This command returns k=7 and now I need to deal with the term:

12*diff(u(x),x$7)^(3/2)*diff(u(x),x$2)^3

Now my question begins. How can I get

1) The non-derivative coefficient of this term? (answer is 12)

Can we define dependencies of a variable after using the variable? For example, let us take,

f:=2*T+x^2;

Here, T has no dependencies. What should we do to make it dependent of x and y without redefining the whole thing as f:=2*T(x,y)+x^2;

and, can we do this for a whole matrix or vector?

Let us say that we have a code shown below:

restart:
with(DifferentialGeometry):
DGsetup([x,y],M):
e[1]:=A*ExteriorDerivative(x);
e[2]:=A*ExteriorDerivative(y);
simplify(e[1] &wedge e[1]+e[1] &wedge e[2]);

the output of this code is

I have a set of partial differential equations and one unknown function f(u,v) which must contain u*Heaviside(u) and v*Heaviside(v) multiplications. Heaviside(u) is the Heaviside step function for the parameter u and it is already defined in Maple.

The solution should come in terms of these multiplications, that is, u or v, or Heaviside(u) or Heaviside(v) cannot occur alone.

I tried a solution of the form,