Ok, I'm working through some dilution/accretion problems in my ODEs book (not homework), all of them centered around draining brine from a tank. The author illustrates the method for solving the problem when you're adding more brine to the tank, and the total water level stays the same, you simply separate the variables. The author also illustrates the method for solving the problem when the water level is changing, but you're not adding more brine to the tank. Again you simply separate the variables.(adsbygoogle = window.adsbygoogle || []).push({});

And that's it, that's all my book explains. It doesn't explain at all what to do when you're both changing the water level and adding more brine to the tank. The author doesn't evenhintat a method for solving it:

Adding brine, but not changing the water level:

100 gallon tank, 3 gals/min brine flow in at 2 lbs of salt per gallon, 3 gals/min of the mix flow out.

dx = 6dt (brine) - (x/100)3dt.

dx/(x-200) = -.03dt.

Separable, hooray.

Not adding brine, changing the water level:

100 gallon tank, 2 gals/min fresh water flow in, 3 gals/min of the mix flow out.

dx = (x/(100-t))3dt.

dx/x = (3/100-t)dt

Again, separable.

Adding brine, changing the water level:

100 gallon tank, 3 gals/min brine flow in at 2lbs of salt per gallon, 2 gals/min of the mix flow out.

dx = 6dt - (x/(100+t))2dt

That doesn't look very separable to me....

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# Dilution problem

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