Unformatted text preview: when the tank is completely ±lled. Recall that the ODE describing the amount of salt in the tank is: dx dt = F 1 c in ( t )-F 2 x V ( t ) , where F 1 (l/s) and F 2 (l/s) are in²ow and out²ow rates, V ( t ) (in l) is the volume of the solution at time t , and c in ( t ) (in kg/l) is the concentration of salt in the solution at the input of the tank. 5. Consider the following population model: dp dt = p (1-p ) , p (0) = p > . (a) Solve this initial value problem. (b) Sketch the direction ±eld and discuss what happens to solutions when t → ∞ . Does your answer depend on the value of p ? * Instructor: Patrick De Leenheer....
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- Summer '06
- Trigraph, Boundary value problem