I just updated to Maple 2020

interface(version)

Standard Worksheet Interface, Maple 2020.0, Windows 10, March 4
   2020 Build ID 1455132

Physics:-Version()
         The "Physics Updates" package is not installed

My question is: For new Maple 2020 installation, should one go and install latest Physics package from the cloud, which I see is at version 619 now, or is it allready included in the new Maple 2020?

I was trying this in Maple to check Mathematica's result, and got this error. But googling and the link Maple gives lead to nothing.

Any one knows why Maple gives this error message here?

restart;

phi:=Pi;
A := <
          <0, 0, exp(I*k1) + m1, exp(I*k2) + m2>|
          <0, 0, exp(I*phi)*(exp(-I*k2) + m2), exp(-I*k1) + m1>|
          <exp(-I*k1) + m1, exp(-I*phi)*(m2 + exp(I*k2)), 0, 0>|
          <exp(-I*k2) + m2, exp(I*k1) + m1, 0, 0>
     >:
LinearAlgebra:-Eigenvectors(A)

Error, (in LinearAlgebra:-Eigenvectors) multiplicity mismatch

fyi, Mathemtica's result is

ClearAll[k1, m1, m2, k2];
Phi = Pi;
H = {{0, 0, Exp[I k1] + m1, Exp[I k2] + m2}, {0, 0, 
    Exp[I Phi] (Exp[-I k2] + m2), Exp[-I k1] + m1}, {Exp[-I k1] + m1, 
    Exp[-I Phi] (m2 + Exp[I k2]), 0, 0}, {Exp[-I k2] + m2, 
    Exp[I k1] + m1, 0, 0}};
Eigenvectors[H]

I tried tracing in Maple, but so far no useful result:

infolevel[all]:=5;
LinearAlgebra:-Eigenvectors(A)

.
.
.
simplify/size: [1/(2+m1^2+m2^2+2*m1*((1/2)*exp(I*k1)+(1/2)*exp(-I*k1))+2*m2*((1/2)*exp(I*k2)+(1/2)*exp(-I*k2)))^(1/2) exp(-I*k1) exp(-I*k2) exp(I*k1) exp(I*k2) _t[1] _t[2] m1 m2 k1 k2]
simplify/size: [exp(-I*k1) exp(-I*k2) exp(I*k1) exp(I*k2) m1 m2 _t[1] _t[2] k1 k2]
simplify/size: [1/(2+m1^2+m2^2+2*m1*cos(k1)+2*m2*cos(k2))^(1/2) exp(-I*k1) exp(-I*k2) cos(k1) cos(k2) _t[1] _t[2] m1 m2 k1 k2]
simplify/do: applying  commonpow  function to expression
simplify/do: applying  power  function to expression
simplify/do: applying simplify/size function to expression

Error, (in LinearAlgebra:-Eigenvectors) multiplicity mismatch

Maple 2019.2.1 on windows

I'd like to solve this ODE

But not sure how to write it in Maple. In Mathematica, this is what I do

ClearAll[F, x, y, t];
ode = D[F[x[t], y[t]], x[t]]*D[x[t], t] + D[F[x[t], y[t]], y[t]]*D[y[t], t] == 0;
DSolve[ode, F[x[t], y[t]], {x[t], y[t]}]

and it gives

In Maple, I tried

ode:=diff(F(x(t),y(t)),x(t))*diff(x(t),t)+diff(F(x(t),y(t)),y(t))*diff(y(t),t)=0

Error, invalid input: diff received x(t), which is not valid for its 2nd argument

ode:=D[1](F)(x(t),y(t))*diff(x(t),t)+D[2](F)(x(t),y(t))*diff(y(t),t)=0;
dsolve(ode,F(x(t),y(t)))

Error, (in dsolve) expected the indeterminate function as, say, F(x) where x is of type "name" - and also cannot be a procedure name. Received: [F(x(t), y(t))]

What is the correct way to write this in Maple?

Do you agree this solution given by Maple is not correct?

restart;
pde := diff(u(x,t),t)+diff(u(x,t),x)=0;
bc  := D[1](u)(0,t)=0;
ic  := u(x,0)=exp(-x^2);
sol:=pdsolve([pde,ic,bc],u(x,t)) assuming x>0,t>0;
pdetest(sol,pde)

Result of pdetest should be zero.

I think the PDE itself is not well posed (I copied it from different forum to see what Maple does with it). But still the solution clearly does not satisfy the PDE itself for x not zero. 

Maple 2019.2.1 with Physics version 573

Hello;

Maple 2019.2.1 on windows 10

Is there a trick to make inttrans:-fourier(erf(x),x,k) return the Fourier transform of the error function? Now, using Maple 2019.2.1 it returns unevaluated. But direct application of Fourier transform integral does return the correct result. So why inttrans does not work? 
 

Download erf.mw