7. Solution by Undetermined Coefficients
The method of undetermined coefficients provides a systematic approach to solve non-homogeneous linear differential equations with constant coefficients, particularly applicable to functions like polynomials, exponentials, and trigonometric functions. This chapter outlines the conditions for employing this method, details the steps for finding particular solutions, and offers illustrative examples. It emphasizes the relevance of this method in practical engineering applications, particularly in civil engineering contexts such as structural analysis and mechanical vibrations.
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Sections
Navigate through the learning materials and practice exercises.
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7.4.1Example 1: Exponential Forcing Function
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7.4.2Example 2: Polynomial Forcing Function
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7.4.3Example 3: Trigonometric Forcing Function
What we have learnt
- The method of undetermined coefficients is effective for specific types of non-homogeneous functions.
- Solving the homogeneous equation is the first step before guessing a form for the particular solution.
- Adjustments may be necessary when the trial solution overlaps with the complementary function.
Key Concepts
- -- Complementary Function
- The solution to the homogeneous part of a differential equation.
- -- Particular Integral
- A specific solution to a non-homogeneous differential equation that accounts for the non-homogeneous part.
- -- Undetermined Coefficients
- A method used to find the particular integral by assuming a trial solution with unknown parameters.
Additional Learning Materials
Supplementary resources to enhance your learning experience.