NAME NetID MATH 285 E1 F1 Exam 1 A September 19 2014 Instructor Pascaleff Problem Possible Actual INSTRUCTIONS Do all work on these sheets 1 20 2 20 3 20 4 20 5 20 Total 100 Show all work 1 1 20 points Consider the differential equation dy xy dx Which of the following graphs could be a solution curve of this equation Circle all that apply 2 2 20 points An object moves along a one dimensional axis Its motion is descibed by a function x t It is subjected to an acceleration given by a t 1 sin t Suppose that at t 0 the velocity is zero v 0 0 What is the net change in position between t 0 and t 1 That is what is x 1 x 0 3 3 20 points Find the general solution valid for x 0 of dy x4 2y dx x Hint Linear equation integrating factor 4 4 20 points Consider the equation dy 2 y y2 dx x Use the substitution u y 1 to transform this equation into a linear equation for u Do not solve the resulting equation the purpose of this problem is merely to transform the original equation for y into one for u 5 5 20 points A metal ball has been heated to 1000 C It is placed into a bath of ice water at 0 C After 5 seconds it has cooled to a temperature of 1000e 10 C approximately 0 045 C Suppose now that the metal ball is heated again to 1000 C but instead it is placed into boiling water at 100 C How long will it take to reach a temperature of 200 C In both situation the cooling process is governed by Newton s law of cooling dT k T A dt where A is the temperature of the water and k is a constant 6 This page is for work that doesn t fit on the other pages Please indicate the problem that the work goes with 7
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