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First-Order Linear Differential Equation
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[QUOTE="lee_sarah76, post: 4644502, member: 488758"] [h2]Homework Statement [/h2] A 400-gallon tank initially contains 200 gallons of water containing 2 parts per billion by weight of dioxin, an extremely potent carcinogen. Suppose water containing 5 parts per billion flows into the top of the tank at a rate of 4 gallons per minute. The water in the tank is kept well mixed, and 2 gallons per minute are removed from the bottom of the tank. How much dioxin is in the tank when the tank is full? [h2]Homework Equations[/h2] I'm going to use D(t) as the amount of dioxin. [h2]The Attempt at a Solution[/h2] dD/dt = (5)(4) - 2*(D(t)/(200+2t)) Using an integrating factor of t + 100, and the initial condition of D(0) = 2, I got that D(t) = (10t[SUP]2[/SUP] + 2000t + 200)/(t+100) But when using t = 100, I get the answer to be 1501 ppb instead of the more appropriate 4.25 ppb. Where did I go wrong? [/QUOTE]
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First-Order Linear Differential Equation
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