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2302-practice-mid4

# 2302-practice-mid4 - a 2 xy ′-y = 0 b x 2 y ′′-2 xy...

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MAP 2302, Fall 2011 — Midterm 4 Review Problems 1 The exam will cover sections 8.3, 8.4, and 8.5. All topics from this review sheet or from the suggested exercises are fair game. 1 Find the first four terms in a power series expansion at x = 0 for a general solution to the given differential equation. a. y + ( x + 2) y = 1. b. y - sin( x ) y = 0. c. e 2 x y - y = e x . d. y ′′ + 4 y = 0. e. y ′′ - xy + x 4 y = sin x . 2 Find the general solution for the following differential equations.
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Unformatted text preview: a. 2 xy ′-y = 0. b. x 2 y ′′-2 xy ′ + y = 0. c. x 2 y ′′ + y = 0. 3 Find all singular points o± the ±ollowing di²erential equations and classi±y them as regular or irregular. a. ( x 2-1) y ′′ + xy ′ + 2 y = 0. b. x 3 ( x 2 + 1) y ′′ + xy ′-y = 0. c. ( x 2-2) y ′′ + √ 2 y ′-sin( x ) y = 0....
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