Now, equation (1) is first order linear differential equation
We know that solution of first order linear differential equation is given by
Now, solving equation(2) by using I.F.
Now, using y(1)= 1 in equation (3)
Now, putting value of c in equation (3)
Hence, solution of given differential equation is
A large tank is partially filled with 100 gallons of fluid in which 10 pounds of
salt is dissolved. Brine containing ½ pound of salt per gallon is pumped into
the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out
at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank
after 30 minutes.