Section 5.1 & 5.2

Section 5.1 & 5.2 - Differential Equations Texas...

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Unformatted text preview: Differential Equations Texas A&M University Math 308, Spring 2008 c circlecopyrt F. Dos Reis Sections 5-1, 5-2 Exercise 1. Two large tanks, each holding 100L of liquid, are interconnected by pipes, with liquid flowing from tank A into tank B at a rate of 3L/min and from B into A at a rate of 1L/min . The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2kg/L of salt flows into the tank A at a rate of 6L/min . The (diluted) solution flows out of the system from tank A at 4L/min and from tank B at 2L/min . If, initially, tank A contains pure water and tank B contains 20kg of salt, determine the mass of salt in each tank at time t greaterorequalslant 0. Definition: The symbol D is used instead of d d t . y ′′ − 3 y ′ + 2 y = 0 is written D 2 y − 3 Dy + 2 y = 0 The product D times D is interpreted as the composition by itself. Exercise 2. Show that • ( D + 1)(2 D 2 − 1) = 2 D 3 + 2 D 2 − D − 1 • ( xD − 1)( D + 1) negationslash = (...
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This note was uploaded on 06/24/2009 for the course MATH 308 taught by Professor Comech during the Spring '08 term at Texas A&M.

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Section 5.1 & 5.2 - Differential Equations Texas...

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