Slope field: Solving a differential analytically can be difficult or even impossible. However, there is a graphical approach you can use to learn a lot about the solutions of a differential equation. Consider a differential equation of the form y\\' = F(x, y)

where F(x, y) is some expression in x and y. At each point (x, y) in the xy-plane where F is defined, the differential equation determines the slope y\\' = F(x, y) of the solutions in the domain of F, then these line segments form a slope field, or a direction field, for the differential equation y\\' = F(x, y). Each line segment has the same slope as the solutions curve throught that point. A slope field shows the general shape of all the solutions and can be helpful in getting a visual perspective of the directions of the solutions of a differential equation.