Answer:
Therefore
Step-by-step explanation:
Given that, a large tank contains 700 gallons of pure water.
At a time t , A(t)is the amount of salt in the tank .
The differential equation of rate of change of salt is
First we find and
=(concentration of salt ).(input rate of brine)
=(3 lb/gal).(7 gal/ min )
=21 lb/min
Since the rate of solution which is pumped out is same rate of pumped in..
= (the concentration of salt in the tank).(output rate)
lb/min
lb/min
Therefore,
....(1)
Here and Q = 21
The integrating factor of the differential equation is
=
Multiply the integrating factor the both sides of ODE of (1)
Integrating bot sides
[c is an arbitrary constant]
At the initial time, the tank contains 700 gallons of pure water.
It means A(0)=0
Putting A=0 ,t=0
Therefore