Subjects differential equations

Phase Portrait 727D86

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1. The problem is to understand how to plot a phase portrait using GeoGebra. 2. A phase portrait is a graphical representation of a dynamical system's trajectories in the phase plane. 3. To plot a phase portrait in GeoGebra, you typically need to define the system of differential equations. 4. Use the 'Differential Equation' tool or input commands like \texttt{\text{DSolve}} or \texttt{\text{SlopeField}} in GeoGebra's CAS or Graphics view. 5. For example, for a system \( \frac{dx}{dt} = f(x,y) \) and \( \frac{dy}{dt} = g(x,y) \), input these functions. 6. Then use the slope field or vector field tools to visualize the direction of trajectories. 7. You can also plot solution curves by selecting initial points and using the integral curve tool. 8. This process helps visualize stability and behavior of equilibria in the system.