The differential equation of the first order

... prescribes the slope at each point of the plane (or at each point of a certain region of the plane we call the field").... a differential equation of the first order... can be conceived intuitively as a problem about the steady flow of a river: Being given the direction of the flow at each point, find the streamlines.... It leaves open the choice between the two possible directions in the line of a given slope. Thus... we should say specifically "direction of an unoriented straight line" and not merely "direction."

Mathematical Methods in Science (1977)