Can someone help? I have a PDE system for two unknown functions, $f(x,y,t)$ and $g(x,y,t)$
$$a_1(t)\frac{\partial f(x,y,t)}{\partial x} + a_2(t)\frac{\partial f(x,y,t)}{\partial y} + a_3(t)\frac{\partial f(x,y,t)}{\partial t} + a_4(t) f(x,y,t)+a_5(t)\frac{\partial g(x,y,t)}{\partial x} = 0$$
$$b_1(t)\frac{\partial g(x,y,t)}{\partial x} + b_2(t)\frac{\partial g(x,y,t)}{\partial y} + b_3(t)\frac{\partial g(x,y,t)}{\partial t} + b_4(t) g(x,y,t)+b_5(t)\frac{\partial f(x,y,t)}{\partial y} = 0$$
Can this be simplified somehow? Both $x$ and $y$ are functions of $t$, $$x=x(t),$$ $$y=y(t)$$ What is the best approach to solving it? I have access to Maple (symbolic PDE solver), but I was thinking I should first simplify the PDE system. Maple can easily take a lot of time solving it and I would much rather simplify it if I can. $$a_i(t)$$ and $$b_i(t)$$ can be rational or linear functions of $t$.