Differential Equations › Section C · Second order differential equations › Topic C.9
Undetermined coefficients
For the inputs met most often in practice, such as constants, polynomials, exponentials, sines and cosines, a particular solution can be found by an educated guess with unknown coefficients. The method is quick and purely algebraic, as long as you know what to guess and when to adjust it.
In this topic
- Guessing with a purpose
- When the method works
- The basic guesses
- Worked example: a cosine input
- Worked example: a polynomial input
- When the guess fails: the modification rule
- Worked example: an input that matches y_c
- Products and sums
- Worked example: writing the guess
- Common mistakes to avoid
- Key takeaways
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