Thanks for the general guidelines; they should definitely prove helpful. I really appreciate your assistance. As you point out, it probably would have been better for me to post the full code at the start.

My code is solving a nonlinear PDE using a perturbation technique. At each order, I generate a set of equations that must all be satisfied. This was working fine for a few loops of the program; for instance I generated the following set of equations, and pdsolve was able to handle it perfectly:

restart:
# Does work
eqs := {2*`A__3,2`(t__1,t__2,t__3) = 0, 6*`A__3,3`(t__1,t__2,t__3) = 0, 2*`B__3,2`(t__1,t__2,t__3) = 0, 6*`B__3,3`(t__1,t__2,t__3) = 0, -2*diff(_F3(t__2,t__3),t__2) = 0, -_F3(t__2,t__3)^3+2*_F3(t__2,t__3)*diff(_F2(t__2,t__3),t__2) = 0, diff(theta(t__0,t__1,t__2,t__3,x),t__0) = 1, diff(theta(t__0,t__1,t__2,t__3,x),t__1) = 0, diff(theta(t__0,t__1,t__2,t__3,x),t__2) =diff(_F2(t__2,t__3),t__2), diff(theta(t__0,t__1,t__2,t__3,x),t__3) =diff(_F2(t__2,t__3),t__3), diff(theta(t__0,t__1,t__2,t__3,x),x) = -1, diff(theta(t__0,t__1,t__2,t__3,x),x) =-diff(theta(t__0,t__1,t__2,t__3,x),t__0), _F3(t__2,t__3) <> 0, theta(t__0,t__1,t__2,t__3,x) <> 0}:
vars := {`A__3,2`(t__1,t__2,t__3), `A__3,3`(t__1,t__2,t__3), `B__3,2`(t__1,t__2,t__3), `B__3,3`(t__1,t__2,t__3), _F2(t__2,t__3), _F3(t__2,t__3), theta(t__0,t__1,t__2,t__3,x)}:
pdsolve(eqs,vars);

However, this particular loop generates the following set of equations which throws the above mentioned error:

restart:
# Doesn't work
eqs :={-2^(1/2)/_F4(t__3)^(1/2)*diff(_F4(t__3),t__3) = 0, 2*2^(1/2)*_F4(t__3)^(1/2)*(diff(_F4(t__3),t__3)*t__2+diff(_F5(t__3),t__3)) = 0, 6*`A__4,3` (t__1,t__2,t__3) = 0, 12*`A__4,4`(t__1,t__2,t__3) = 0, 2*`B__4,2`(t__1,t__2,t__3) = 0, 6*`B__4,3`(t__1,t__2,t__3) = 0, 12*`B__4,4`(t__1,t__2,t__3) = 0, 4*_F4(t__3)^2+2*`A__4,2`(t__1,t__2,t__3) = 0, diff(theta(t__0,t__1,t__2,t__3,x),t__0) = 1, diff(theta(t__0,t__1,t__2,t__3,x),t__1) = 0, diff(theta (t__0,t__1,t__2,t__3,x),t__2) = _F4(t__3), diff(theta(t__0,t__1,t__2,t__3,x),t__3) = diff(_F4(t__3),t__3)*t__2+diff(_F5(t__3),t__3), diff(theta(t__0, t__1,t__2,t__3,x),x) = -1, diff(theta(t__0,t__1,t__2,t__3,x),x) = -diff(theta(t__0,t__1,t__2,t__3,x),t__0), 2^(1/2)*_F4(t__3)^(1/2) <> 0, theta(t__0, t__1,t__2,t__3,x) <> 0}:
vars := {`A__4,2`(t__1,t__2,t__3), `A__4,3`(t__1,t__2,t__3), `A__4,4`(t__1,t__2,t__3), `B__4,2`(t__1,t__2,t__3), `B__4,3`(t__1,t__2,t__3), `B__4,4`(t__1,t__2 ,t__3), _F4(t__3), _F5(t__3), theta(t__0,t__1,t__2,t__3,x)}:
dsolve(eqs,vars);

As you has mentioned, I have a number of "pdes" here which aren't actually differential equations; I was surprised it didn't work here, as this method has worked fine for me before (as shown above).

Perhaps it would be better to remove the non-differential equations from the system. Unfortunately, since this list of equations is generated automatically, I don't know how to pull those out and "solve" them seperately (ultimately, I want a list of solutions to run **assign** on).