SOLUTION: Please any help will be grateful with this problem . A 400 gallon tank is filled with pure water . A salt solution with a concentration of 14g/gal flows into the tank at a rate 6g

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Question 1071996: Please any help will be grateful with this problem .
A 400 gallon tank is filled with pure water . A salt solution with a concentration of 14g/gal flows into the tank at a rate 6gal/min . The thoroughly mixed solution is drained from the tank at a rate 6gal/min .
A)Write an initial value problem for the mass of the salt .
B)Solve the initial value problem .


This is how i started it . I might be wrong . Please feel free to correct anything i did .
dy/dt = (rate in )-(rate out)
rate in =(14g/gal)(6gal/min)=84g/min
rate out =(y(t)g/400gal)(6gal/min)=3y(t)/400(g/min)
dy/dt=84-3y(t)/200 . Then i don't know how to finish it .

Thank you .
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Yes, that is the correct setup.
dy%2Fdt%2B%283%2F200%29y=84
So the general solution dy%2Fdt%2Bky=0 is,
y=ae%5E%28bt%29
and the particular solution dy%2Fdt%2Bcy=d is,
y=d%2Fc
Work those through to get the answer using the initial condition.