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3 cards from this section. Quick, good the night before a test.
What is the general form of a linear non-homogeneous differential equation?
Look for terms involving y, its first and second derivatives and a function f(x).
Identify a suitable f(x) for the method of undetermined coefficients.
Think about functions you can easily differentiate or integrate.
What is a complementary function in the context of differential equations?
Focus on what happens when f(x) = 0.
Can the method of undetermined coefficients be used for ln(x)?
Consider the categories of functions suitable for this method.
Investigate the differential equation y'' + 2y' + 5y = 10e^x + sin(2x). Provide the general solution.
Pay attention to the form of each term to set up your trial solutions.
Given the equation y'' - 3y' + 2y = x*cos(x) + 4e^x, decompose the problem into finding complementary and particular solutions, and combine them.
Keep track of your trials—f(x) will provide hints for the forms.
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