#### bug in [detools,dchangevar] in maple v.4 (8.9.97)

Maple R4 answers:

I expected:

In the online help about Dchangevar, the ﬁrst example in ”Examples/Additional examples”
gives:

Maple answers, after some simplication:

Answer expected:

It seems that Dchangevar mistakes if the order of the diﬀerential equation is >=2 and if the change of
variable is not linear.

Is there a bug in Maple or in my mind?

The bug is removed in Maple V Release 5. (U. Klein)

As an alternative, you can use PDEtools[dchange], which is able to perform non-linear changes of
variables and also in PDEs. In your example,

PDEtools is a package distributed in the Share Library of Maple R4. The last version of PDEtools is
found at

http://lie.uwaterloo.ca/pdetools.html (Canada)

or

http://dft.if.uerj.br/pdetools.html (Brazil)

I get the same as you do! There must be a bug in Dchangevar.

I checked the variable transformation with a procedure of my own ( vsubs ) and could conﬁrm the
supposed results of G. Thomas and also reproduce the wrong answers that Dchangevar gave
:

I have noticed the bug in DEtools a long time ago. I had sent Maple a worksheet summarizing where the
bug occurs, but never received any follow up.

If I recall, what I had observed was that DEtools did not know how to apply the chain rule
properly.

I discovered this while trying to get maple to perform the same set of calculations I had
done on paper. Had the change of variable worked properly, I would have reduced my ODE
to one which has the hypergeometric function as a solution. Otherwise, Maple could not
solve it. I was trying to reproduce some work I had found in a paper I was using for my
research.