@Preben Alsholm 

Regarding the subscript sort:
I was probably not clear enough (sorry, English is not my first language). I always said “subscript” and meant literal subscripts, no indexes. (see also the different color in my initial question). So, the minus has no effect.

regarding the derivative sort:
Kitonums replacement of the add command works.
I’ve also tried your interessting idea. It works with the first example, but try something else.
(e.g.: b*y(t)+a*diff(y(t), t)). It causes an error in the “S:= seq….” line: “invalid subscript selector”

Overall I’ve to say, I’m impressed of your support, so far I have learned something and it is incomprehensible why the specialized “sort”-command doesn’t have the capability to handle this with simple options (like “diff” in collect).
I think, sorting of those things in equations is not unusual, isn’t it.

I’m studying Engineering and I use Maple 18 in “Document Mode” since I've believed the promise Maple makes copy and paste to a word processing tool obsolete. Ok, it turned out, this promise was a lie. However, by the time, I’ve learned many workarounds which makes this goal very tricky but almost possible.

So, because my documents always have some requirements regarding usage of variables, structure of equations etc, I depend on (literal) subscripts, atomic variables and sorting.

You already have Maple 2016, have you noticed real improvements in Document mode, should I update?

Hi guys, I really thank you for your ideas! They look pretty smart and might solve my problems ... with two little exceptions. I’ve spent over an hour this afternoon to change your code, but I don’t get it.

@Carl Love: My Maple installation shows the result of your “subscript-sort” ascending and not descending.

@Kitonum

Everything works except the “add” construct.
I get the error: “… add expects 2 arguments, but received 1”
(Maple Help mentions always two arguments. How is that supposed to work?)

Could you help me once more?

Hi guys, I really thank you for your ideas! They look pretty smart and might solve my problems ... with two little exceptions. I’ve spent over an hour this afternoon to change your code, but I don’t get it.

@Carl Love: My Maple installation shows the result of your “subscript-sort” ascending and not descending.

@Kitonum

Everything works except the “add” construct.
I get the error: “… add expects 2 arguments, but received 1”
(Maple Help mentions always two arguments. How is that supposed to work?)

Could you help me once more?

Hi guys, I really thank you for your ideas! They look pretty smart and might solve my problems

... with two little exceptions. I’ve spent over an hour this afternoon to change your code, but I don’t get it.

@Carl Love My Maple installation shows the result of your “subscript-sort” ascending and not descending.

@Kitonum

Everything works except the “add” construct. I get the error: " add expects 2 arguments, but received 1”

(Maple Help mentions always two arguments. How is that supposed to work?)

Could you help me once more?

@vv 

..is there also a way to convert this series expression via an comand into "cos"?

convert(expr,trig) apparently does not work

@vv ...that looks simple! Key is, to do the division inside the series function and to use the right eqn parameter for "series" of course