I solved this linear constant coefficients ode by hand, and wanted to use Maple to check my solution.

dsolve works with no problem. I wanted to check the particular solution on its own, so called DEtools:-particularsol(ode,y(x)); but was surprised it hangs.

Why would DEtools:-particularsol(ode,y(x)); hang, when dsolve gives the complete solution (including particular solutin ofcourse) right away?  It is 7th order ODE. But nothing special. Linear and constant coefficients. Since dsolve solves it right away, I expected DEtools:-particularsol to have no problem as well.

restart;
ode:=diff(y(x),x$7)-2*diff(y(x),x$6)+9*diff(y(x),x$5)-16*diff(y(x),x$4)+24*diff(y(x),x$3)-32*diff(y(x),x$2)+16*diff(y(x),x)=exp(2*x)+x*sin(x)+x^2;

dsolve(ode);  #no problem.

#this hangs. Why?
DEtools:-particularsol(ode,y(x));

Download particular_sol.mw

I was saying to myself today, that one nice thing in Maple, is that it has good type system so one can check type of arguments aginst wrong types being used in the call.

So I was surprised when I called ArrayTools:-AllNonZero  using list as argument, where this function is supposed to accept only Matrix,Vector or Array. And it worked.  But it gave wrong answer at the same time.

Am I doing something wrong here? Should not have this call failed to go through?

restart;
interface(warnlevel=4);
kernelopts('assertlevel'=2):

A:=[0,0,0];
ArrayTools:-AllNonZero(A)

Maple replied 

                       true

But 

A:=Array([0,0,0]);
ArrayTools:-AllNonZero(A)

Now Maple gives the expected result  false

The question is why Maple did not detect the wrong type? Should it have detected wrong type?

And why it even gave wrong answer (but this is not as important, since the call should not be allowed in first place).

btw, this applied to all the other API's listed

I found a new strange thing with odetest that I have not seen before.

Would you say that these two solutions are the same or not?

They look the same to me.  One just have all the terms on one side, that is all.

Why would Maple odetest verify the first one but not the second? I did not know that all terms have to be on one side before. Is this documented somewhere?

Please see worksheet below.

Download odetest_issue_oct_18_2020.mw

Using solve on this example:

restart;
eq:=x^3 - 3*x^2 + 3*x - 1=0;
solve(eq,x);

gives solution x=1, with multiplicty 3

              1, 1, 1

When using PDEtools:-Solve

restart;
eq:=x^3 - 3*x^2 + 3*x - 1=0;
solve(eq,x);
PDEtools:-Solve(eq,x);

it gives

         x = 1

How can one make it show x=1, x=1, x=1 ?

Found that only when using PDEtools:-Solve(eq,x,numeric) it gives 

           x = 1., x = 1., x = 1.

How to make it do the same without using numeric?

Maple 2020.1.1

What is the reason that error accepts its arguments without being inside paranthesis? This is different from all other Maple functions I've seen. For example, both these below work the same

f := proc (x) 
     if x<0 then 
        error "invalid x: %1", x; 
     else 
        x^(1/2); 
     end if 
end proc:

And

g := proc (x) 
     if x<0 then 
        error("invalid x: %1", x); 
     else 
        x^(1/2)
     end if 
end proc:

One can't do for other Maple functions. For example sin x  gives an error. It must be sin(x)

Looked at help page for error and did not see something about this difference.