Direction Fields (Slope Fields)

• A plot of short line segments (or arrows) drawn at various points in the xy-plane showing the slope of the solution curve at that point
• Suggests the appearance of a family of solutions for the DE
• Allows us to determine asymptotic behavior (${\lim }_{x\to \pm \infty }y(x)$)
• A single solution curve that passes through a point in the direction field must follow the flow pattern

Method of Isoclines

• Isocline = set of points that all have the same slope
• Plug in values for $\frac{dy}{dx}$ and then draw that slope along the line it graphs