Final answer:
It is true that solving a system analytically before creating a phase portrait makes the process easier and typically more accurate, as explicit solutions provide a clear basis for constructing the graphical representation.
Step-by-step explanation:
In the context of differential equations and dynamical systems:
it is true that if a system can be solved, it is generally easier to find the explicit solution before creating a phase portrait. The creation of a phase portrait can be more straightforward when the solutions to the system are known since it allows for direct plotting of the trajectories. Phase portraits are a graphical representation of the different trajectories that solutions to a system of differential equations can take.
They provide a qualitative view of the system's behavior over time. When solving systems analytically, such as linear systems with constant coefficients, explicit solutions often lead to a clear and accurate construction of the phase portrait. Analytical techniques, when applicable, are typically more precise than graphical solutions because they are not subject to the limitations of scale and resolution that graphical methods face.