MATH2860U:
Chapter 3
1
MODELLING WITH FIRST-ORDER
DIFFERENTIAL EQUATIONS
Linear Models (Section 3.1 of Zill and Cullen, pg. 83)
Recall:
Earlier, we discussed the process of setting up linear models.
We also discussed
how to solve linear differential equations.
Let’s put all of this together and solve some linear DEs arising in applications.
Application:
A 2000L tank contains 70 L of water with 0.3 kg/L of dissolved salt.
Water containing 0.1 kg of salt per litre enters the tank at a rate of 8 L/min.
The solution
is kept thoroughly mixed and drains from the tank at a rate of 6 L/min.
How much salt
will be in the tank after 5 min?

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