(3pts) Verify that is a solution of the differential equation
(5pts ea.) Solve the following differential equations
(8pts) A large tank is partially filled with 100 gallons of fluid in which 10 pounds of salt is dissolved. Brine containing pounds of salt per gallon is pumped into the tank at a rate of 6 gallons per minute.. The well mixed solution is then pumped out at a slower rate of 4 gallons per minute.. Find the number of pounds of salt in the tank after 3 minutes. If the capacity of the tank is 400 gallons, find the number of pounds of salt in the tank just as it overflows.
(4pts) Given that is a two parameter family of solutions of on the interval can you find a solution of the differential equation satisfying the initial conditions Is the solution unique? Do your answers contradict the existence and uniqueness theorem? Explain.