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Undetermined coefficients vs. Variation of Parameters

  1. Jan 13, 2008 #1

    Regarding the two procedures: undetermined coefficients and variation of parameters, can both procedures be used interchangeably - meaning they both solve (non-homogeneous linear equations)?

    Does one method work better in certain situations, if so which method is preferred when?

    How can one know when to use which method?

  2. jcsd
  3. Jan 13, 2008 #2


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    If I recall correctly, undetermined coefficients only works if the inhomogeneous term is an exponential, sine/cosine, or a combination of them, while Variation of Parameters always works, but the math is a little more messy.
  4. Jan 14, 2008 #3


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    nicksause is correct. The "possible solutions" to a linear equation with constant coefficients must be: exponential, polynomial (he forgot those!), sine or cosine, or combinations of those. "Undetermined Coefficients" only works if the right-hand side of the equation is one of those.

    For example, y"+ y= ln(x) or y"- 2y'+ y= tan(x) cannot be done by undetermined coefficients. They can be solved by variation of parameters- though you might not be able to do the resulting integral.
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