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 µ ( t ) = exp ±R (2 / 25) dt ² = 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 ³ 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...
View
Full Document
 Spring '10
 Hald,OH
 Math, Physics, Differential Equations, Linear Algebra, Operations Research, Algebra, Equations, Optimization, mathematical model

Click to edit the document details