A tank contains 1000 gal of water in which 200 lb of salt is dissolved. 50 gal of brine, each gallon containing (1 + cos t) lb of dissolved salt, runs into the tank per minute. The mixture, kept uniform by stirring, runs out the same rate. Find the amount of salt in the tank at any time t.
The Attempt at a Solution
dc1/dt + dc2/ dt = 0
Since dc1/ dt = - dc2/ dt then dc1/ dt + 50c/1000 = 0
∫dc/c = -∫1/20 dt
Lower limit for dc/c is 200 and upper limit is c. Then, C = 200e^.05t
But, no (1+cos(t)). Please help