@tomleslie 

+1 for the ormap. I did not know about it. But I am afraid your method does not work for general expression. For example 

                    sin(x)*(x*y)^(1/3)+3

Now it does not match. The input expression can be anything as I mentioned in my question and my reply to Carl above. The idea is that I need to detect a pattern inside a larger expression, which can be as complicated as one wants. 

@Carl Love 

Nothing wrong with using has() in this case. But I was just making a simple example. (if has() can do everything patmatch can, then patmatch would not be needed :)  So may be this can be considered as an exercise to do with has() did but using patmatch instead.

For example, suppose I want to detect for  radical with power between say 1/6 and 1/3, as in

 sin(x)*(x*y)^(1/3)  or sin(x)+(x*y)^(1/6)

Then I would write 

restart;
expr:= sin(x)*(x*y)^(1/3);
if patmatch(expr,a::anything*(b::anything*x*y)^(c::anything),'la') then
    print("Pattern match");
    assign(la);
    if c >= 1/6 and c<= 1/3 then
       print("found pattern");
    else
       print("did not find pattern");
    fi;
 else
   print("did not find pattern");
 fi;

And would have to do it again using

if patmatch(expr,a::anything+(b::anything*x*y)^(c::anything),'la') then

Actually, it gets worst. If I want to ckeck for SOMETHING +*  my_pattern +* SOMETHING which is most general.I'd have to make 3 cases, not just 2

if patmatch(expr,a::anything+(b::anything*x*y)^(c::anything)+d::anything,'la') then
...
if patmatch(expr,a::anything+(b::anything*x*y)^(c::anything)*d::anything,'la') then
...
if patmatch(expr,a::anything*(b::anything*x*y)^(c::anything)+d::anything,'la') then
...

So, yes has() works in the example I posted, but this was just a simple example. I still want to use patmatch and tell Maple that the operator between the terms can be  * or + without having to duplicate code for each case, that is why I asked.

@DJJerome1976 

Maple is weak in this area.

It does not even have a function that returns the real domain of a function, similar to Mathematica's  https://reference.wolfram.com/language/ref/FunctionDomain.html

Maple can give one a list of singularties, sure, and using icont() or using discont() on the real line. But this is only half the story. 

Maple needs the equivlant of Mathematic'a FunctionDomain, which was introduced almost 6 years ago by now.

May be Maple in the next version will have something like this. This must be hard to implement, else Maplesoft would have such a function by now I would think.

@ecterrab 

"Anyway, for the example you indcate, in my opinion the degree is 1, not 2, since it is linear in the highest derivative"

I think the degree is 2 and not 1, since the powers have to be integers on all derivative first before deciding:

This is how I learned it at school. Any way, thanks again for the link and the help.

@ecterrab 

Thanks. But I can't figure how to use it to tell me for example that  (1+diff(y(x),x)^2)^(3/2) = diff(y(x),x$2) has degee 2. I do not understand what a differential polynomial or a differential ideal or a differential polynomial ring is or how to make them from the ODE.These are a little advanced topics for me, I have not studied these yet.

@Rouben Rostamian  

I am sorry, I do not understand why you said that the degree is not defined for the first example you show.

The first one has degree one, since the power on the highest derivative is one. Using Carl's code given in answer below confirms:

ode:= diff(x(t),t$2)+sin(x(t))=0;
ODEdegree(ode);

           1

The degree becomes 2 in this case

ode:= diff(x(t),t$2)^2+sin(x(t))=0;
ODEdegree(ode);

    2

@Rouben Rostamian  

https://en.wikipedia.org/wiki/Degree_of_a_differential_equation

"In mathematics, the degree of a differential equation is the power of its highest derivative, after the equation has been made rational and integral in all of its derivatives"

I need to find this during parsing of ODE to help me decide if I can solve it or not.

@Thomas Richard 

thanks. But it is strange, that Maple, being the best CAS in ODE's does not have a buildin function to find the degree of an ODE in addition to the order.

May be this is something Maplesoft could add for the next release.

First, you do not need to write “c://Users//hello//Documents//h.m”. it is either “c:/Users/hello/Documents/h.m” or  “c:\\Users\\hello\\Documents\\h.m”

But have you tried to open h.m  yourself from outside Maple? does it work? And have you tried to check what security there are on the folder itself?

@Carl Love 

There is still a case which is given a problem. This is what Maple returns solutions as sequence of lists. Here is example

Download bug_june_25_2019_2.mw

I had to put {} around the result, since it is sequence, in order to make it a list.  But now it becomes a list of lists, and this is why it gives an error. I'll see if I can find a work around for this case.

@Carl Love 

Hello; I found a small bug. Sometimes pdsolve returns a solution which of type 'function', and hence your is_solution_trivial function now fails on it. Here is an example

Download bug_june_25_2019.mw

I add `function` as one of allowed types to accept, and now it seems to work OK. I hope this was the correct way to fix this.

Download bug_june_25_2019_fixed.mw

Maple 2019.1

@Carl Love 

Thanks. Your functions worked very well. Verified on Maple 2019.1

@tomleslie 

Nice. But I do not think you need max there.

I rewrote your function a little to make it easier for me to understand (I do not like the style of using () over many lines, I find it hard for me to read, I've also seen others use the style you are using here).  (ps. I understand code style is a personal thing. All what I am saying is that I find this harder for me to read, that is all).

DETools:-difforder worked without using max in the following

restart;
get_order:=proc(expr,fun,var)
  local the_list,i;
  the_list := convert( indets(expr, function),list);
  PDETools:-difforder(select( i-> has(i, diff(fun,var)),the_list))
end proc:

Now 

f:= 2*y*(diff(x(t), t))^2+3*(diff(x(t), t$3))-3*x*(diff(y(t), t));
get_order(f, y(t),t);
get_order(f, x(t),t);

Returned 1 and 3 also.

@Carl Love 

Thanks. I verified your solution also works very well on Maple 2019.1

@acer 

Thanks. I verified your code works with no problem on 2019.1