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

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.

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



u := (x, y, z) -> f(x^2+y^2+z^2)

proc (x, y, z) options operator, arrow; f(x^2+y^2+z^2) end proc


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)






u := (x, y, z) -> C*f(x^2+y^2+z^2)*exp(x+y+z)

proc (x, y, z) options operator, arrow; C*f(x^2+y^2+z^2)*exp(x+y+z) end proc


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)






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')

U(x, y, z) = exp((1/2)*x^2*_C2)*exp(_C1*x)*exp((1/2)*y^2*_C2)*exp(_C1*y)*_C3*_C5*_C4*exp((1/2)*z^2*_C2)*exp(_C1*z)


combine(rhs(%), exp)






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