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3 cards from this section. Quick, good the night before a test.
What graphical feature characterizes solutions with real distinct roots?
Think about the upward and downward growth in the absence of oscillation.
What happens in the graph when dealing with repeated roots?
Consider how it approaches equilibrium.
When the roots of a second-order differential equation are real and distinct, the solution will:
Focus on how the graphs of distinct roots appear.
True or False: Repeated roots lead to oscillatory solutions.
Think about what happens when roots are the same.
Given a second-order differential equation with complex conjugate roots, derive the general solution and describe its behavior over time.
Focus on extracting the general form applicable for complex roots.
Illustrate the advantages of using software tools in depicting solutions to second-order equations. Provide an example.
Think about specific features in plotting software that aid in visualizing these equations.
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