exam1 - ODE, Math S3027D Section 001 Summer 2008 Exam 1...

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ODE, Math S3027D Section 001 Summer 2008 Exam 1 Name: June 12, 2007 Do all problems, in any order. Show your work. An answer alone may not receive full credit. No notes, texts, or calculators may be used on this exam. Problem Possible Points Points Earned 1 10 2 10 3 10 4 10 5 10 6 10 7 10 TOTAL 70 1
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1. (10 points) Find a particular solution of y 00 + 6 y 0 + 13 y = e - t . 2
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2. (10 points) Find the general solution to ty 0 = 4 t - 3 y . 3
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(10 points) Salt water enters a 20 gallon tank at a rate of 5 gal/min and leaves at the same rate from the bottom. A rotor keeps the solution well mixed. Write x ( t ) for the number of pounds of salt in the tank at time t . Suppose at t = 0 the tank is full of fresh water. Suppose that the concentration of salt water being added is q ( t ) lb/gal (lb=pound). (a) Write the ODE governing x ( t ) ( t measured in min). (b) Suppose that the concentration q ( t ) of the salt water being added varies periodically with time according to the expression g ( t ) = 2 + sin t . Solve the ODE from part (a) using this g ( t ). 4
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This note was uploaded on 10/18/2011 for the course MATH S3027D taught by Professor Peters during the Spring '11 term at Columbia.

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exam1 - ODE, Math S3027D Section 001 Summer 2008 Exam 1...

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