Is it possible to delete all tags with the +Manage Tags option? I mean, when I write a post I am always forced to enter a tag.

I checked a few other posts and all had not tags.

dsolve/IC/apply_IC comes to the conclusion that -c__1=0 for the first IC and c__1=0 for the second IC.

Therefore c__1=-c__1=0 which leads to the solution y(x)=c__2*x^2

restart;
trace(`dsolve/IC/apply_IC`);
ode := x^2*diff(y(x), x $ 2) - 2*y(x) = 0;
ic := y(0) = 4, D(y)(0) = -1;
sol_no_IC := dsolve(ode);
sol_with_IC := dsolve([ode, ic]);

I think that the applied method to determine the integration constants (which does not devide by zero) is not appropirate to handle ICs that lead to singularities. Those ICs should be rejected or a warning should be issued.

The fact the ICs produce a valid solution for the ode is a coincidence that makes this case hard to understand.

Update: I have deleted my reasoning about odetest which was based on a wrong assumption on the expected output of odetest for ICs. odetest correctly indicates that something does not fit together.

I add here the crucial step that removed the singularity from the computation of c__1

This step avoids devision by zero errors

and returns an output that I interprete now like this:

At the inital point x=0 the solution of the ode has only one integration constant that could not be determined with ICs.

Prebens reply shows that the integration constant is a parameter which can be determied if one point of the solution for x>0 is given. It is therefore not an initial value problem any more.

I am wondering how this insight (if correct) could be provided to the user.

@janhardo 

ODESteps is in line with nm statements

@acer 

Thank you. This is indeed of interest. I did not know about this option. Strange tha t?solve,details is not refering to it

@MaPal93 

Either

1. lambda_1*delta_1+lambda_2*delta_2-lambda_3*delta_3>0 and theta<0     or
2. lambda_1*delta_1+lambda_2*delta_2-lambda_3*delta_3<0 and theta>0

is correct but not complete (does not cover all possibilities). What is missing is

• lambda_1*delta_1+lambda_2*delta_2-lambda_3*delta_3>0 and theta<0     or
• lambda_1*delta_1+lambda_2*delta_2-lambda_3*delta_3<0 and theta>0

       and

       (lambda_1*delta_1+lambda_2*delta_2-lambda_3*delta_3<0* theta) < -(-lambda_1-lambda_2-lambda_3)*theta^2

This is what mmcdara tried to express.

The tricky part with inequaltities is that some valid combinations are easily over looked.

For the same reason solve issues warnings. Technically solve could have gone through all combinations as I did. I assume that solve does not do it for the simple reason that evaluation time increases exponentially with each case to investigate (not to mention the amount of output).

Your case was rather easy. There might be cases where solutiosn are only possible with other assumptions like delta__1< delta__2. Whether solve can always find those....

Using my worksheet you can find equivalent solutions solving for other parameters which might be more suitable for you.

@sand15 

Interesting way. I vote up. When I do whattype(r[2]), I get the type list which should have removed all elements from r but it did not.

Is whattype not specific ennough (i.e. does not tell us about "subtypes").

@acer 

The colon convention for help topics would definitely have helped to avoid wrong conclusions on syntactical equivalence. The colon convention should be introduced everywhere. Since this takes time some explanations in the description of the help system could clarifiy that there are also older converntions.

I have tried to reconstruct the searches that I have performed for command extensions and indexed procedures. For extensions I tried / to find out more about uses of /

Similarly, I tired [] to find out more about uses of square brackets.

Here, not even the help topic ?indexed is listed. I don’t now whether this page would be an appropriate place to mention indexed procedures. At least one could point to other resources providing more information on that topic. I also cannot see a reason not to officialise the term indexed procedure.

@nm  No change with physics update

@Thomas Richard 

Same for me with Maple default settings (fresh installation, no special settings)

@acer 

It takes time to catch-up with your replies because they require close studying and lead to more questions.

If you do not mind, one of them would be: Are indexed procedures stored in tabels? Or: is this a special type of data structure?

Thank you for your time!

@acer 

Simplify[sqrt] is listened under “See also” on the simplify help page. On the other hand, simplify,details lists this option under “See also” as simplify/sqrt. This suggested equivalence to me. If additionally, equivalence is assumed between library calls and extensions, improper use of command options is almost unavoidable.

I now understand why my command option trials gave such an inconsistent outcome.

I am attracted by indexed procedures/commands because this seems to be the only way in function composition to pass arguments. Now I learn that not all options can be used as an index. Is there a way to check what index (if any) is implemented?

Your explanations are more than valuable. In this case I feel that part of it should be documented because even after careful studying the documentation, at the best, it (the explanations) could be guessed. Not my prefered way to work with a language.

@Preben Alsholm 

I have taken the first examples from ?simplify,sqrt and ?combine. I did not expect that they work without options. Probably some recent enhancements that did not propagete to the examples.

I modified the examples in the hope to get a better understanding. This explains part of the confusion.

The indexed procedure example is good. I have not seen it this way in the documentation. The closest I found were  "Objects in Indexed Function Calls" in the programming guide but this is more about object oriented programming I guess.

Thank you

@acer 

Thank you for the explanation. I was mislead by the scale, which gave me the impression as if a function call took place.

I do not get the same if I do

E := t -> 0;
diffeq := D(C)(t) = E;
sol:=dsolve({diffeq, C(0) = 0}, {C(t)}, numeric);
plots:-odeplot(sol,t=0..10);

The comment about linear fits was more of general nature and towards measured (noisy) data in combination with piecewise linear fits. This potentially could cause problems with solvers trying to integrate with a certain accuracy.

@sand15 

Thank you. There must be more than one path to deal with the unavoidable case analysis depending on the relations between a, b, c, d, t.  I have updated my response for a case where b abd c cannot be freely chosen.

Since the location of the pole at x=-t/d with respect to m and n is important I would (for a new attempt) rewrite the problem this way

(f*x^2 + g*x + h)/(x + p);
                            2          
                         f x  + g x + h
                         --------------
                             x + p     

to have one parameter less to deal with. Maybe helpfull if the OP is interesed to reduce the set of possible solutions.

@acer
Now its clear. There is use for functional operators and unapply, which both can produce the same output.
Thank you for the detailed answer.