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Question: is it possible to solve this PDE In Maple 2018?

Question:is it possible to solve this PDE In Maple 2018?

nm 9874 Maple 2018
differential-equation pde pdsolve
March 23 2018
1

Does any one know of a trick to make Maple solve this PDE using pdsolve?

restart;
pde:=diff(u(x,t),t)+diff(u(x,t),x)=0;
bc:=u(0,t)=0;
ic:=u(x,0)=x;
sol:=pdsolve({pde,ic,bc},u(x,t));

I have tried all HINTS and assumptions and Maple just returns () as solution.

Mathematica solve this as follows

ClearAll[u,x,t];
pde=D[u[x,t],t]+D[u[x,t],x]==0;
bc=u[0,t]==0;
ic=u[x,0]==x;
sol=DSolve[{pde,ic,bc},u[x,t],{x,t}]

 

Heavidside theta is basically a unit step function.

 
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