2302f11-mid1 - NAME MAP 2302 — Elementary Differential...

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Unformatted text preview: NAME : MAP 2302 — Elementary Differential Equations — Fall 2011 September 12, 2011 Midterm 1 Instructions: This is a closed book exam and no notes are allowed. You are not to provide or receive help from any outside source during the exam except that you may ask the instructor for clarification of a problem. You have 50 minutes and you should attempt all problems. • Print your name in the space provided. • Sign the FERPA release on the next page only if you wish your exam returned in lecture. • Calculators or other computing devices are not allowed. • Except when indicated, you must show all work and give a reason (or reasons) for your answer. A correct answer with incorrect work will be considered wrong. FERPA Release: Because of privacy concerns, I will not return your graded exams in lecture without your permission. If you want me to return your exam in lecture, please sign on the line indicated below. Otherwise, you may collect your exam during my office hours. SIGN HERE: . Problem Points 1 25 2 25 3 25 4 25 Total 100 Score 1. (25) Indicate whether each of the following differential equations are separable or linear. Indicate the integrating factor for the linear differential equations. Do not attempt to solve these equations. You do not need to show any work. a. dy = 2xy sin(x + y ). dx Separable? No Linear? b. Yes Yes No If yes, integrating factor: dy = 2y sin x − cos x. dx Separable? No If yes, integrating factor: Yes No Linear? Yes No If yes, integrating factor: Separable? Yes No Linear? e. Yes Separable? d. No Linear? c. Yes Yes No If yes, integrating factor: Separable? Yes No Linear? Yes No If yes, integrating factor: x2 − y dy =√. dx x dy = xy sin x. dx x3 ln y dy = . dx y2 1 2. (25) Solve the differential equation dy cos y + 2xy = . dx x sin y − x2 2 3. (25) Make an appropriate substitution in order to solve the differential equation dy y = + ex y 2 . dx x 3 4. (25) Solve the initial value problem 1 y (0) = . e dy xy = ; dx ln y 4 5 ...
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2302f11-mid1 - NAME MAP 2302 — Elementary Differential...

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