2065f09review1

# 2065f09review1 - Math 2065 Section 1 Review Exercises for...

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Math 2065 Section 1 Review Exercises for Exam I The syllabus for Exam I is Chapter 1 and Section 2.1. A copy of Tables 2.1 and 2.2 on Pages 103 and 104 will be provided with the exam. You should bring your own paper for the exam, since space will (in general) not be provided on the exam paper for answers. You will need to show all relevant work in order to receive partial credit. 1. Determine if each of the following equations is separable (yes or no), and/or linear (yes or no). Do not solve the equations! (a) y 0 = y 2 ¡ t (b) t 2 y 0 = 1 ¡ 2 ty (c) yy 0 = 3 ¡ 2 y (d) y 0 y = y ¡ t (e) ty 0 = y ¡ 2 ty (f) ( t 2 + 3 y 2 ) y 0 = ¡ 2 ty (g) y 0 = ty 2 ¡ y 2 + t ¡ 1 (h) t + y 0 = y ¡ 2 ty 2. Find the general solution of each of the following diﬁerential equations. You must show your work. (a) y 0 + 2 y = 0 (b) y 0 + 2 y = 3 e t (c) y 0 ¡ y = e 3 t (d) y 0 + 2 ty = t (e) y 0 + 3 t y = sin t t 3 (f) y 0 = t 2 y (g) ty 0 = p 1 ¡ y 2 (h) y 0 = y 2 + 4 (i) 2 ty 2 ¡ 3 + (2 t 2 y + 4) y 0 = 0 (j) ty 0 = 2 te t ¡ y + 6 t 2 (k) y 0 + y = e t y 2 1

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3. Solve each of the following initial value problems. You must show your work.
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## This document was uploaded on 12/28/2011.

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2065f09review1 - Math 2065 Section 1 Review Exercises for...

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