1. (Exercise 1.4.11) Initially 5 grams of salt are dissolved in 20 liters of water. Brine with concen tration of salt 2 grams of salt per liter is added at a rate of 3 liters a minute. The tank is mixed well and is drained at 3 liters a minute. How long does the process have to continue until there are 20 grams of salt in the tank? 2. Consider the equation, dy _ 4 (a) Find all critical points. (b) Classify their stability. (c) What range of initial conditions results in solutions with limH00 y(t) = %. What about limlHDO y(t) = 'T'o' and lirntnoO y(t) = 3%? 3. Consider the equation, dy _ 2 dt _ ay :9 7 (a) Again consider the cases a 0. In each case nd the critical points, draw the phase line, and determine whether each critical point is asymptotically stable, metastable(semistable)1, or unstable. (b) In each case sketch the direction eld and several solutions of the equation in the typlane