111_pdfsam_math 54 differential equation solutions odd

111_pdfsam_math 54 differential equation solutions odd -...

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Exercises 3.2 fnd x ( t ). We can determine the concentration oF salt in the frst tank by dividing x ( t )bythe its volume, i.e., x ( t ) / 60 kg/gal. Note that the volume oF brine in this tank remains constant because the flow rate in is the same as the flow rate out. Then output rate 1 = (3 gal / min) · ± x ( t ) 60 kg / gal ² = x ( t ) 20 kg / min . Since the incoming liquid is pure water, we conclude that input rate 1 =0 . ThereFore, x ( t ) satisfes the initial value problem dx dt = input rate 1 output rate 1 = x 20 ,x (0) = x 0 . This equation is linear and separable. Solving and using the initial condition to evaluate the arbitrary constant, we fnd x ( t )= x 0 e t/ 20 . Now, let y ( t ) denote the mass oF salt in the second tank at time
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.

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