# Question:harmless assumptions changes the form of the final solution from pdsolve for wave pde

## Question:harmless assumptions changes the form of the final solution from pdsolve for wave pde

Maple 2018

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.

Compare

```#example 19, wave pde, on string left end fixed, right end moving, with source, no initial velocity
restart;
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.

```Physics:-Version();