trying some examples from 209970-Exact-Solutions-For-PDE-And-Boundary--Initial-Conditions-2018
I noticed some answer change when adding assumptions which should not really cause the answer to change. Numerically, both answers seem to be the same. But one is series solution and the other with assumptions added uses integrals.
In wave pde on string where left end at x=0 and adding assumptions x>0,t>0 to pdsolve should produce the same form and it does on some problems but no on others.
#example 19, wave pde, on string left end fixed, right end moving, with source, no initial velocity
pde := diff(u(x, t), t$2) = 4*diff(u(x, t), x$2)+(1+t)*x;
bc := u(0,t)=0,u(Pi,t)=sin(t);
ic := u(x,0)=0,eval(diff(u(x,t),t),t=0)=0;
sol:=pdsolve([pde, bc,ic],u(x,t)); #1
sol:=pdsolve([pde, bc,ic],u(x,t)) assuming t>0; #2
sol:=pdsolve([pde, bc,ic],u(x,t)) assuming x>0; #3
sol:=pdsolve([pde, bc,ic],u(x,t)) assuming t>0,x>0; #4
(1,2,3) above give same answer which is
but (4) gives
Tried random points and numerically they are the same (set the sum to n=100 to evaluate).
my question is why would adding no assuming, or adding t>0 on its own or adding x>0 on its own give same answer, but adding t>0,x>0 at same time give such a different looking soution.
I typically adding such assumptions to be safe, but here it seems to had some side effect I have not noticed before.
"C:\Maple_updates\Physics+Updates.maple", 2018, December 22,
10:41 hours, version in the MapleCloud: 265, version installed in this computer: not installed
Maple 2018.2, X86 64 WINDOWS, Nov 16 2018, Build ID 1362973