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2 cards from this section. Quick, good the night before a test.
Explain the role of the complementary function in the method of undetermined coefficients.
Consider its definition in relation to the differential equation.
What is the trial solution if f(x) = sin(ax)?
Think about the forms we use for trigonometric functions.
What is the first step in the method of undetermined coefficients?
Think about what comes first in the sequence.
True or False: The method of undetermined coefficients can be applied to any non-homogeneous function.
Remember the conditions listed for the application.
Solve the equation y'' - 4y' + 4y = 3e^{2x}. Identify your steps.
Be careful with the double root; it changes how you write your complementary function!
For the equation y'' + 2y' + y = sin(x), find the general solution.
You might need to adjust your trial solution if overlap occurs.
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