SOLUTION: For this problem A is the amount of salt in the tank. If a tank contains 250 liters of liquid with 11 grams of salt. A mixture containing 11 grams per liter is pumped into the tan

Algebra ->  Equations -> SOLUTION: For this problem A is the amount of salt in the tank. If a tank contains 250 liters of liquid with 11 grams of salt. A mixture containing 11 grams per liter is pumped into the tan      Log On


   

Question 1184506: For this problem A is the amount of salt in the tank.
If a tank contains 250 liters of liquid with 11 grams of salt. A mixture containing 11 grams per liter is pumped into the tank at a rate of 5 liters/minute. The mixture is well-mixed, and pumped out at a rate of 6 liters/minute. The amount of salt in the tank satisfies the differential equation.
((6A)/(250-t))-55+A'=0
Rewriting this as a linear differential equation we get A'+((6A)/(250-t))=55
A)The integrating factor is
B)And the solution is

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!

(A) The integrating factor is e%5E%286%2Aint%28dt%2F%28250-t%29%29%29+= e%5E%28-6%2Aln%28250-t%29%29+=+%28250-t%29%5E%28-6%29

(B) The solution is A%28t%29+=+11%28250+-+t%29+-+1.122x10%5E%28-11%29%2A%28250-t%29%5E6