# Question:Maybe not the right place to tell about that?

## Question:Maybe not the right place to tell about that?

Maple

I'm presently interested in PDE and I have just discovered the impressive work Nasser Abbasi,has done, and keeps doing, concerning the solution of PDE benchmarks with Maple and Mathematica.
https://www.12000.org/my_notes/pde_in_CAS/pdse3.htm

It seems that the result Maple returns for the test case below is not the general solution.

• 4.19 first order PDE of three unknowns
problem number 19
(from example 3.5.4, p 212, nonlinear ode’s by Lokenath Debnath, 3rd edition)

It is rather simple to see that any spherical function u(x, y, z) =f(x^2+y^2+z^2) is a solution of the PDE.
Then any function of the form u(x, y, z) = f(x^2+y^2+z^2) * exp(x+y+z) *C1 (C1 being any constant) is also a solution.
Maple returns only the solution u(x, y, z) = exp(C2*(x^2+y^2+z^2)) * exp(x+y+z) * C1

 > restart:
 > u := (x, y, z) -> f(x^2+y^2+z^2)
 (1)
 > expr := (y-z)*diff(u(x, y, z), x)+(z-x)*diff(u(x, y, z), y)+(x-y)*diff(u(x, y, z), z)
 (2)
 > simplify(%);
 (3)
 > u := (x, y, z) -> C*f(x^2+y^2+z^2)*exp(x+y+z)
 (4)
 > expr := (y-z)*diff(u(x, y, z), x)+(z-x)*diff(u(x, y, z), y)+(x-y)*diff(u(x, y, z), z)
 (5)
 > simplify(%);
 (6)
 > pdsolve((y-z)*diff(U(x, y, z), x)+(z-x)*diff(U(x, y, z), y)+(x-y)*diff(U(x, y, z), z)=0, U(x,y,z),'build')
 (7)
 > combine(rhs(%), exp)
 (8)
 >