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MATH2860U:
Chapter 3
1
MODELLING WITH FIRSTORDER
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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View Full DocumentMATH2860U:
Chapter 3
2
Application:
A radioactive substance decays at a rate proportional to the amount
present, and half the original quantity is left after 1500 years.
If the original quantity is
Q
0
, how much remains after 2000 years?
[Source:
Elementary Differential Equations with Boundary Value Problems
by William F. Trench]
Application:
A 7volt battery is connected to a series circuit in which the inductance is 2
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 Spring '10
 Kidnan

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