Partial derivatives

Hi, my question is about part iii of this question, I don’t know why but I just don’t get it, I t seems to lead me to a=b=0 which just seems wrong,

Anyone know what to do for it? Here is my working for the other two question auf it’s relevant, not a clue if they are correct or not

ii) looks ok and differentiating f(x,y) gives the original P and Q. For iii) using ii) you must have
arctan(...) = c
so ... You could check by solving
P dx + Q dy = 0
directly though they want you do use the solution for f(x,y).

So does it want be to find c?, I’m not sure what to do exactly, does df=0 imply that f(x,y) Is constant and then I just solve for y?

Its just the integral curves. It wants ypu to find the function y(x) which will contain a constant.

So just rearrange 0= -arctan(…) + c for y?