1) Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some equations may be more than one kind. a) b) c) 2) Solve the given Bernoulli equation by using an appropriate substitution. 3) A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved. Brine containing 1 pound of salt per gallon is pumped into the tank at a rate of 5 gal/min. The well mixed solution is then pumped out at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank after 30 minutes. 4) Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially there are 60 grams of A and 60 grams of B, and for each 2 grams of A, 3 grams of B is used. It is observed that 20 grams of C is formed in 10 minutes. What is the limiting amount of C after a long time? 5) Find an interval centered about x = 0 for which the given initial value problem has a unique solution. 6) Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. 7) Use the superposition principle to find particular solutions of the following equations a) b)