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Unformatted text preview: out. Therefore, the concentration of salt at time t is x ( t ) / 100 kg/L and output rate = x ( t ) 100 (kg / L) 8 (L / min) = 2 x ( t ) 25 (kg / min) . Then the equation (1) yields dx dt = 0 . 4 2 x 25 dx dt + 2 x 25 = 0 . 4 , x (0) = 0 . 5 . This equation is linear, has integrating factor ( t ) = exp R (2 / 25) dt = e 2 t/ 25 , and so d ( e 2 t/ 25 x ) dt = 0 . 4 e 2 t/ 25 e 2 t/ 25 x = 0 . 4 25 2 e 2 t/ 25 + C = 5 e 2 t/ 25 + C x = 5 + Ce 2 t/ 25 . Using the initial condition, we Fnd C . . 5 = x (0) = 5 + C C = 4 . 5 , 103...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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