Ordinary Diff Eq Exam Review Solutions 26

# Ordinary Diff Eq Exam Review Solutions 26 - 28 1 Solutions...

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Unformatted text preview: 28 1 Solutions Integrating and simplifying gives . The initial condition implies so . Now the brine solution in Tank 1 has concentration and ﬂows into Tank 2 at a rate of liters per minute. Thus L g input rate for Tank 2: input rate min L g . min L g g output rate for Tank 2: output rate . min L min The initial value problem for Tank 2 is thus: Simplifying and putting this equation in standard form gives The integrating factor is again (as for the Tank 1 equation) Thus multiplying by the integrating factor gives . Integrating and simplifying gives The initial condition implies so 33. Let and denote the amount of salt in respectively, at time . The volume of ﬂuid at time and Tank 2 is . L input rate for Tank 1: input rate min output rate for Tank 1: output rate Tank 1 and Tank 2, in Tank 1 is g L L min g . min g . The initial value problem for Tank 1 is thus min Simplifying this equation and putting it in standard form gives g L ...
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