Practice Step 2: Guess The Form Of The Particular Integral (7.3.2)

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6 sample questions

Question 1.
What is the trial solution if f(x) = sin(3x)?
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Remember it's sine and cosine.
Question 2.
If f(x) = 5x^2 + 3x, what's the trial solution?
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This is a polynomial function.
3Question 3.
What is the initial guess for the particular integral of e^(3x)?
- Ae^(3x)
- Ax*e^(3x)
- A*cos(3x) + B*sin(3x)
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Think of the function form.
4Question 4.
True or False: The trial solution needs to be modified if it overlaps with the complementary function.
- True
- False
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Consider the implications of having the same terms.
Question 5.
Solve the differential equation y'' - 3y' + 2y = e^(x) + x. Find the particular integral with appropriate adjustments.
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Review the forms of f(x) and identify overlaps.
Question 6.
Given y'' + y = 4sin(x) + e^(2x), determine the adjustments needed for your trial solutions.
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Focus on function types appearing in y_c.

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