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Math Help - Regular Singular Points

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    Regular Singular Points

    The problem is taken from "Elementary Differential Equations and Boundary Value Problems," 8th Edition. By Boyce. Section 5.4 (Page 271), problem 1. The problem states to find all singular points of the given equation and determine whether each one is regular or irregular. How would I approach this problem?

    The problem is x*y'' + (1 - x)*y' + x*y = 0
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    Quote Originally Posted by fudawala View Post
    The problem is taken from "Elementary Differential Equations and Boundary Value Problems," 8th Edition. By Boyce. Section 5.4 (Page 271), problem 1. The problem states to find all singular points of the given equation and determine whether each one is regular or irregular. How would I approach this problem?
    What was the problem?

    A differential equation of the form: P(x)y'' + Q(x)y' + R(x)y = 0 is said to have a "regular singular point," x_0, if:

    \lim_{x \to x_0} (x - x_0) \frac {Q(x)}{P(x)} < \infty

    AND

    \lim_{x \to x_0} (x - x_0)^2 \frac {R(x)}{P(x)} < \infty

    That is, if both the above limits are finite for the point x_0, then x_0 is said to be a regular singular point

    Now try the problem and post the solution if you wish, so we can check it


    Note: We say x_0 is a singular point if \frac {Q(x)}{P(x)} and/or \frac {R(x)}{P(x)} are discontinuous functions at x_0. We classify the singular point as "regular" or "irregular" by the method above
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