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Question: Unexpected results from pdsolve

Question:Unexpected results from pdsolve

Rouben Rostamian 8018 Maple 2022
pde pdsolve differential-equations
September 10 2022
2
> 

restart;
> 

pde := diff(u(x,t),t) + u(x,t)*diff(u(x,t),x) = 0;

diff(u(x, t), t)+u(x, t)*(diff(u(x, t), x)) = 0

These are all wrong:

> 

pdsolve({pde,u(x,0)=f(x)});
pdsolve({pde,u(x,0)=sin(x)});
pdsolve({pde,u(x,0)=erf(x)});

u(x, t) = 0

u(x, t) = 0

u(x, t) = 0

But these ones are correct:

> 

pdsolve({pde,u(x,0)=exp(x)});
pdsolve({pde,u(x,0)=x});

u(x, t) = LambertW(t*exp(x))/t

u(x, t) = x/(t+1)

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