differential equations

Question

A tank contains 360 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t)

 of grams of salt in the tank at time t.

A(t) = __________________g

Answer 1

A'(t) = 6 - A(t)/60;

A'(t) + 1/60A(t) = 6; M = e^∫1/60dt = e^t/60; A'(t)e^t/60 + 1/60A(t)e^t/60 [= 6e^t/60; d/dt(e^t/60A(t)) = 6e^t/60;

A(t)e^t/60 = ∫6e^t/60dt; A(t) = 360e^t/60 + C; A(t) = 360 + Ce^-t/60;

At t = 0 A(0) = 50; 50 = 360 + C; C = - 310; A(t) = 360 - 310e^-t/60g