I was trying to verify some solution to pde in textbook using Maple. The book gives the Cauchy data for this first order PDE in the form that Maple does not like when I used it as input. Here is an example

When I typed

pde:=u(x,y)*(x+y)*diff(u(x,y),x)+u(x,y)*(x-y)*diff(u(x,y),y)=x^2+y^2;
ic:=u(x,2*x)=0;
pdsolve([pde,ic],u(x,y))

Maple complained

Error, (in PDEtools:-Library:-NormalizeBoundaryConditions) unexpected 
occurrence of the variables {x} in the 2nd operand of u(x, 2*x) in the given initial conditions

In Mathematica it accepts such form of Cauchy data:

pde=u[x,y]*(x+y)*D[u[x,y],x]+u[x,y]*(x-y)*D[u[x,y],y]==x^2+y^2;
ic=u[x,2*x]==0;
DSolve[{pde,ic},u[x,y],{x,y}]

(I have not verified the above answer is correct or not).

Am I doing something wrong in Maple?

Or is there a trick or option or method to allow Maple to accepts such initial conditions? The book I am looking at has many problems where Cauch data is given on such form (i.e. u=0 on specific curve or in 3D on some specific surface). Here is another example

Which I'd like write its initial conditions as u(x,1/x)=0 but can not.

I could ofcourse solve the pde without these initial conditions, and then post process the answer to find the constants of integration from the Cauchy data given. But it will be nice if Maple would accept the IC as is.

Is it considered a bug when pdetest does not give zero for a solution given by pdsolve? 

restart;
pde := x*diff(w(x,y,z),x)+  a*z*diff(w(x,y,z),y)+b*y*diff(w(x,y,z),z)=c:
sol:=pdsolve(pde,w(x,y,z));
pdetest(sol,pde)

Gives

which is not zero.

This is the first time I've seen this happen. 

Maple 2019.1 using Physics version 362

I need to use gamma as a "free" symbol in pde that I pass to pdsolve, so that the latex comes out as \gamma OK in the solution.

in other words, the pde itself uses the symbol gamma (as it is written in the textbook and I want to keep it the same). This gamma is not the known constant gamma. Something similar to using alpha and beta or x and y. 

But gamma in a known constant in Maple and I am worried this will affect some computation inside pdsolve if I use gamma  as known number in the PDE (even though I think it should not change the result of pdsolve as there are no other numbers in the PDE input, I just wanted to be safe).

I am not able to clear gamma

unassign(gamma)  gives error since it is protected.

Is  there a way around this? Should I use wrap the name with 'gamma'  or `gamma` for example? 

Here is an example

pde := a*diff(w(x,y,z),x)+ b*diff(w(x,y,z),y)+c*diff(w(x,y,z),z)= alpha*x+beta*y+gamma*z+delta;

It is the gamma above I am worried about using in the input. What is the correct way to do this?  

I have thought that   D(y)(0)=C1  and  eval(diff(y(t),t),t=0)=C1  mean exactly the same thing which is derivative of y wr.t. "t" evaluated at specific point t=0 is C1.

If you agree they are exactly the same thing, then why dsolve works with both forms used for initial conditions if the option 'series' is not used.

When using the 'series' option, dsolve stops working when using  eval(diff(y(t),t),t=0) form? All else is the same.

ode:=diff(y(t),t$2)+3*diff(y(t),t)+2*y(t)=0;
bc_form_1:=y(0)=C1,eval(diff(y(t),t),t=0)=C2;
bc_form_2:=y(0)=C1,D(y)(0)=C2;
sol1:=dsolve([ode,bc_form_1],y(t));
sol2:=dsolve([ode,bc_form_2],y(t))

Both the above work

But now when I use the 'series' option, the first form stops working!

ode:=diff(y(t),t$2)+3*diff(y(t),t)+2*y(t)=0;
bc_form_1:=y(0)=C1,eval(diff(y(t),t),t=0)=C2;
bc_form_2:=y(0)=C1,D(y)(0)=C2;
sol1:=dsolve([ode,bc_form_1],y(t),'series');
sol2:=dsolve([ode,bc_form_2],y(t),'series')

Is this a bug? 

Just updated to Maple 2019.1  on windows 10.

Maple is very good in solving PDE's. But this specific solution seems way too complicated when compared to Matematica solution, which I verified using Maple pdetest to be correct.

Is there a way to make Maple produce the simpler solution to this pde? simplify does nothing on the solution. May be by using a good HINT or such other option? 
 

Here is screen shot showing the other solution

Download q1.mw