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2 cards from this section. Quick, good the night before a test.
What adjustment is needed when the trial solution overlaps with the complementary function?
Consider how to eliminate duplication.
What is a non-standard right-hand side?
Think of unusual functions.
When faced with repeated roots, how can you modify your guess?
Think about how duplicates are formed.
True or False: The undetermined coefficients method can be used for rational functions like 1/(x+1).
Consider which functions fit standard forms.
Solve the differential equation y′′ + 4y = cos(2x), ensuring to adjust your trial character.
Identify the nature of your complement.
For y′′ − 3y′ + 2y = x^3 sin(x), describe how to approach this using variation instead of undetermined coefficients.
Reflect on core concepts of replacement methods.
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