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http://mathhelpboards.com/math-notes-49/justifying-method-undetermined-coefficients-4839.html

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http://mathhelpboards.com/math-notes-49/justifying-method-undetermined-coefficients-4839.html

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- Jan 26, 2012

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1. In the table, in the $y_{p}(x)$ column for Type I's, an $x^{s}$ seems to have become an $x^{2}$.

2. I would rewrite Equation (3) as follows (you haven't really used operator notation, but have included the test function in your definition of $L$, which is not usual):

$$(3) \quad L[y] \equiv a_nD^{n}+ a_{n-1}D^{n-1}+ \cdots+ a_{1}D+ a_0.$$

You do this later on, so this is more of a consistency thing, I think.

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- Jan 26, 2012

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$$L \equiv a_{n}D^{n}+a_{n-1}D^{n-1}+ \dots + a_{1}D + a_{0},$$

or

$$L[y] = \left( a_{n}D^{n}+a_{n-1}D^{n-1}+ \dots + a_{1}D + a_{0} \right)y.$$

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I truly appreciate your suggestions, and feel the post has been improved because of them.