What is the correct syntax to do this change of variable from the text book:

The problem is that using PDEtools:-dchange, it wants the transformation to have form { old = new}, i.e. x=...  so I can not write  z=g(x) in the transformation. 

For example

ode:= diff(y(x),x$2)+diff(y(x),x)+y(x)=sin(x);
PDEtools:-dchange({z= g(x)},ode,known={x},unknown={z});

Error, (in dchange/info) missing a list with the new variables
And if I first solve for x so that I can write the transformation with x on left side, it still does not work

ode:= diff(y(x),x$2)+diff(y(x),x)+y(x)=sin(x);
PDEtools:-dchange({x=RootOf(g(_Z) - z)},ode,known={x},unknown={z});

Where RootOf(g(_Z) - z) was result of solve(z=g(x),x);

I am sure this can be done in Maple, I just do not know the right syntax to use with dchange.

Maple 2024.2

Is there a trick to make Maple give same result below when using eval and limit?  

Attached worksheet. This comes in context of solving ode  using Laplace. Initial conditions are at zero. And need to solve for the constant of integration. 

It works when using eval, since Dirac(t) becomes Dirac(0), but when using Limit, Dirac(t) becomes zero and the _C1 is lost. I was wondering if limit should also return Dirac(0) like eval?

Download dirac_limit_dec_13_2024.mw

In Latest Maple 2024.2, I found that when doing z:=%  where % is result on integration, causes internal error 

          Error, unexpected result from Typesetting

But when the interface is set to standard, no such error.

This not only happen in worksheet, but also when code is run in command line!

Worksheet below.

Download extended_interface_causes_internal_bug_dec_13_2024.mw

ps. also reported to Maple support

evalindets API says 

             evalindets( expr, atype, transformer, rest )

Where the transformer will be applied on any indents of atype.

But I want to be able to do the opposit, i.e. 

             evalindets( expr, except_this_atype, transformer, rest )

ie. apply the transformer on everything except those of atype.

Here is a concrete example and what I tried.

I get result of apply inverse Fourier transform which can have some terms in it which can not be evaluated. Like this

Y:=(s+1)/s^2+Int(sqrt(s^2),s);
expr:=inttrans:-invlaplace(Y,s,t);

Now I want to evaluate the above at some specific value of t, say t=0 but I do not want change/touch any "t" inside invlaplace(....) function. 

If I just do 

eval(expr,t=0)

So I tried evalindets with flat option and used for atype anything, then inside the transformer, check if op(0,X) is invlaplace (i.e the head), and if so, skip it. But it did not work

Y:=(s+1)/s^2+Int(sqrt(s^2),s);
expr:=inttrans:-invlaplace(Y,s,t);
evalindets[flat](expr,anything,X->`if`( evalb(op(0,X)='invlaplace'),X,eval(X,t=0)));
evalindets[flat](expr,anything,X->`if`( op(0,X)='invlaplace',X,eval(X,t=0)));

Currently what I do to make this to work, is to first replace the "t" inside invlaplace by another unused symbol, then do the eval to change t, then replace the symbol back to t.

Like this, and this works:

Y:=(s+1)/s^2+Int(sqrt(s^2),s);
expr:=inttrans:-invlaplace(Y,s,t);
expr:=evalindets[flat](expr,'specfunc(anything,invlaplace)',X->eval(X,t=T));
expr:=eval(expr,t=0);
expr:=eval(expr,T=t);

Is it possible to do the above using one call to evalindets?  Why did the check I had the above using `if`(...) not work?

It will be really useful if evalindets had option NOT atype,  in addition of just atype.

i.e. tell it to do the transformation on everything except the type given.

Maple 2024.2

When giving invlaplace an input with an Inert integral (becuase it can not be evaluated), it sometimes return 
              Error, (in depends) malformed integral

But sometimes it returns the inverse Laplace of the unresolved integral, which is the expected result.

In both cases, it should just return  inverse Laplace of the unresolved integral.

Below is worksheet showing such case.

Download malformed_intergal_dec_7_2024.mw

Just reported to Maple support also.