2302-practice-mid1

2302-practice-mid1 - Then, solve the equations which are...

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MAP 2302, Fall 2010 — Midterm 1 Review Problems 1 The exam will cover sections 1.2, 1.3, 2.2, 2.3, 2.4, and 2.6. All topics from this review sheet or from the suggested exercises are fair game. 1 Give explicit solutions to the initial value problem dy dx = xy 3 with y (0) = 1, y (0) = 1 / 2 , and y (0) = - 2. Then determine the domains of each of these solutions. 2 Show that every separable Frst-order di±erential equation can easily be converted into an exact equation. 3 ²or each of the following di±erential equations, indicate whether they are separable, linear, or can easily be converted into an exact equation. Note that some equations may be more than one type, while others may not be any of these types.
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Unformatted text preview: Then, solve the equations which are separable, linear, or exact. a. dy dx =-2 xy x 2 + y 2 . b. dy dx = xy sin x . c. dy dx = sin( x + y 2 ). d. dy dx = x-y 2 x . e. dy dx = 5 x 4 cos y + e y . 4 ²or each of the following initial value problems, determine if they have zero, one, or more than one solution(s). You do not need to solve these equations. a. y dy dx + x = 0; y (1) = 0. b. dy dx = 3 y 2 / 3 ; y (0) = 0. c. y dy dx = arctan( x + y ); y (1) = 1. 5 Make an appropriate substitution in order to solve the following di±erential equations. a. dy dx = 2 y x-x 2 y 2 . b. x 2 dy dx = xy-y 2 . c. dy dx = 1 (2 x + y ) e 2 x + y-2....
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This note was uploaded on 12/10/2011 for the course MAP 2302 taught by Professor Tuncer during the Fall '08 term at University of Florida.

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