Two-variable ODEs with one variable fixed

Question

How do you solve variables with $f(x,y)$ where we only take the derivative wrt one of the variables? I presume the other variable can be taken as fixed, but I don't know what changes we need to make to our usual formulas?

e.g. $$f_x(x,y) + f(x,y) = 1$$

Also, how would you use Maple to solve them? If I define an $ode$ and use dsolve, it says "required specification of the indeterminate function".

Answer 1

In maple, you are suppose to use pdsolve to solve a pde not dsolve,

restart;
Eq1:= diff(f(x,y),x)+f(x,y)=1;
pdsolve(Eq1);