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pdsovle - query?

griffgruff 24
November 25 2008
0
The function pdsolve gives different answers depending upon the way the problem is posed. For example:

> PDE1:=a*diff(u(x,t),t)+b*diff(u(x,t),x)-u(x,t)^2=0;
> ans1:=pdsolve(PDE1);

gives:

> ans1 := u(x,t) = b/(-x+_F1(-(-t*b+a*x)/b)*b);

Whilst,

> PDE2:=a*diff(u(t,x),t)+b*diff(u(t,x),x)-u(t,x)^2=0;
> ans2:=pdsolve(PDE2);

which is the same problem but with u(x,t) replaced by u(t,x), gives:

> ans2 := u(t,x) = a/(-t+_F1((-t*b+a*x)/a)*a);

Both are actually correct solutions, as is easily verified by a call to pdetest.

My query is:

1) Why does the Maple solution vary according to how u is specified?
2) is it posible to get Maple to automatically provide both solutions regardless as to how u is specified?

Any help appreciated.

example

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