Suppose that the amount of salt in the mixture be Q.
The volume of mixture at time t will be as follows:
Recall the fact that the concentration of salt will be given as follows:
Also, the rate of gain minus rate of loss will be
Here rate of gain is 0 and rate of loss is
Initially the amount of salt in the mixture is 55 kg. That is,
By the end one 1 hours, t will be 60 minutes.
Thus, the amount of salt in tank after one hour is 21.4913 Kg.
Determine the largest interval in which the initial value problem (t − 3)y ′′ − ty′ + 6y = sin t has unique solution.
y(−3) = 2, y′ (−3) = 1