Graphical ideas are introduced early (e.g., the direction field of figure 1.2, p. 4) and used regularly. Sketching solution graphs of first-order scalar equations (e.g., section 1.2, A Modeling Example; section 2.1, Simple Population Models; section 2.2, Emigration and Competition, etc.) reinforces slope and concavity ideas from calculus, providing an obvious connection with earlier course work that many students find reassuring.
After regular but informal use of direction fields and solution graphs to analyze the projectile model of chapter 1 and the various population models of chapter 2, these ideas are consolidated in section 3.2, Direction Fields and Phase Lines. They are further reinforced in section 3.3, Steady States, Stability, and Linearization.
The phase plane first appears in the analysis of the population models derived in section 2.4, Multiple Species. It is introduced more formally in chapter 7, primarily through the nonlinear pendulum equation, and tied to the geometry of the solutions of constant-coefficient, homogeneous, linear systems in section 8.3, Connections with the Phase Plane.
A maximal treatment of graphical ideas would start with section 1.2, then include all of sections 3.2, 3.3, 7.1-7.3, and 8.3.
A minimal treatment might omit subsection 3.2.3, Phase Lines, tread lightly on the graphical interpretations of stability in section 3.3, and omit section 7.2, Nullclines and Local Linearization, and section 7.3, Limit Cycles and Stability. Conceivably, section 8.3, Connections with the Phase Plane, could be omitted as well, but you would be depriving your students of the two-dimensional punch line that connects analytic and geometric ideas. Without it, differential equations will seem a long shaggy dog story about tricks and special methods.
These graphical results--sketching solution plots, direction fields, phase diagrams, etc.--can obtained through the Graphical tools menu bar selection in DELab.