Maple R4 answers:
In the online help about Dchangevar, the ﬁrst example in ”Examples/Additional examples” gives:
Maple answers, after some simplication:
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
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.