A large tank is filled to capacity with 500 gallons of pure water. Brine (a mixture of salt and water) containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gallons per minute. The well-mixed solution is pumped out at a rate of 10 gallons per minute. Find the number of pounds of salt in the tank at time .
OK. I know that the rate at which the amount of salt is changing inside the tank with respect to time - - is simply the net rate of the amount being pumped in and the amount being pumped out, that is
and I think that
Assuming my is correct, this would imply the DE
which is linear with the integrating factor
So, I have
Am I on the right track?