I dont know what you mean- you might be making this more complicated than necessary.
If you make the substition z=-x, then you have a differential equation of the form
A(z,y) + B(z,y)dz/dy = 0
where [not my favoured notation but Im not familiar with the BBcodething for partial derivatives: anyway it equals -2 in this example]
this is a standard equation with solvable method described in good textbooks I guess .
[ Simpler if you are not familiar with the above: y=-x+C is a solution by inspection, and you can work out C]