In mathematics, a phase line is a diagram that shows the qualitative behaviour of an autonomous ordinary differential equation in a single variable, = (). The phase line is the 1-dimensional form …

This simple diagram tells you roughly how the system behaves. It’s called the phase line. The phase line captures exactly the information we use to get the qualitative sketch of solution …

Phase Lines The nonlinear autonomous equation x' = g(x) can be understood in terms of the graph of g(x) or the phase line. As a parameter in g(x) varies, the critical points on the phase …

Graph Phase Plane: Line width: + -Initial x and y Trace path (or click on the graph)

The phase line diagram of Figure 5.6 also presents the same information as in Table 5.1, but in contrast to Figures 5.3 and 5.4 we need to include two equilibrium solutions. Phase line …

A phase line diagram for the autonomous equation y′ = f(y) is a line segment with labels sink, source or node, one for each root of f(y) = 0, i.e., each equilibrium; see Figure 14. It …

May 15, 2025 · Phase Line Diagram Plot Autonomous Differential Equations Classify Equilibrium Points

Draw the phase line for the following equations for several values of the parameter a. Choose one value of a for every possible qualitatively different phase line.

In the video you have seen how you can construct a phase line from the direction field of a differential equation. You can only draw a phase line when the differential equation is a so …

above, there are two lines: a phase line (the dark one) and a line with a slope of + 1 which passes through the origin. The phase line represents a specific difference equation that mathematically