Question

Use the techniques we've learned involving phase plane to plot a phase portrait of: dx/dt = 2 dy/dt = -3 where the x and y values are between -5 and 5. Then, on the same plot, use drawphase to draw at least three different solution curves. Include the resulting plot in your Word document.

Answer 1

The student was directed on how to create a phase portrait for a system of linear differential equations with constant coefficients and plot at least three solution curves, indicating how different initial conditions will evolve over time.

Step-by-step explanation:

The student is asking how to plot a phase portrait for a system of differential equations and draw solution curves using a graphical method, such as drawphase. The system provided is:

• dx/dt = 2
• dy/dt = -3

Since both equations do not depend on variables x or y, the system describes constant rates of change: x increases at a constant rate while y decreases at a constant rate. To create a phase portrait, one would plot a grid with x and y axes ranging from -5 to 5. At each point in the grid, a small arrow would be drawn representing the direction and magnitude of the vector (2, -3). The entire plane will be filled with parallel vectors pointing in the direction of increasing x and decreasing y.

For the solution curves, one would select various starting points and draw curves that follow the arrow directions, showing how the system's state evolves over time. Because the rates of change are constant, these curves will be straight lines. Drawing at least three solution curves would show how different initial conditions evolve in time according to the system.