Maple knows how to obtain differntials using D.

So typing  D(x*y) it gives   D(x)*y+x*D(y)

But what I want is given as input  D(x)*y+x*D(y) have Maple return back D(x*y)

Nothing I tried work. I tried simplify and convert(...,D) 

I am looking for a function that takes an expression with differentials like the above output, and return, if possible ONE differnetial in the form  D(  f(x,y) )

What I mean, given as INPUT any of these expressions on the RHS in the image below

To return back  the  D(...)  in the LHS above. I know Maple can do it going from the LHS to the RHS. But I want the other way around.

Does Maple support such operations?

Maple 2022.1

To Maple support,. 

fyi,

internal error generated on this ode when trying odetest
 

Download problem_odetest_july_23_2022.mw

What is the correct way to write the explicit solution before calling odetest to verify it on an ode? is it

   sol:= y(x)= the RHS  (1)

or

   sol:= y(x) - the RHS = 0 (2)

I am asking because Maple sometimes gives very different result from odetest depending on which form the explicit solution is written. It is very hard to keep trying different forms each time.  Here is an example below.

Maple 2022.1 on windows 10.   Is this a bug? I do not think it should  make a difference, but it does and I have no idea why. Is there an option or way to make sure the same result is obtained each time regardless how the explicit soltion is written?

I have a theory as to why this might happen: When using (1) odetest sees y(x) on the LHS on its own, and then uses odetest  code internally designed for explicit solution testing.

When using (2), it sees y(x) not on its own on the LHS and it assumes this is then an implicit solution and uses odetest code internally meant for implicit solution testing, hence the difference in output.
 

Download why_different_result.mw

Any one has a trick to show in Maple that  x + sqrt(-2 + 2*sqrt(4*x^2 + 1))*sqrt(2 + 2*sqrt(4*x^2 + 1))/4; is zero for x<=0?

I'd like to get similar simplication as this below but in Maple, But everything I tried so far did not work. I am sure there is a way in Maple, but have not found it yet.

Below is the Maple worksheet

Download show_it_is_zero.mw

I use Int to show some step before evaluating it to become normal int

I'd like to show the following when the integrand is one:

But Int(x) does not work, and Int(,x) gives syntax error. So only choice is to use Int(1,x) which does not look as nice as the above

Is there a trick to use? i.e. when the integrand is one, I want to display it as the first image and not as the second image. This is just to make the Latex look a little nicer only.

I tried few things, but nothing worked so far, as Int needs something there where I want the empty spot to be (There is actually 1 there ofcourse, but I do not want to show the 1).

May be we need a Latex settings for this?  Or interface setting?

Maple 2022.1