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**Unformatted text preview: **DIFFERENTIAL EQUATIONS AND THEIR APPLICATION
and tank 2 contains 250 gal of brine with 14 lb
of salt. Brine containing 3 lb of salt per gallon
enters tank 1 at the rate of 13 gal/s. Mixed
200 gal of brine (salt water) with 55 lb of salt,
brine in tank 1 flows out into tank 2 at the rate
tank 2 contains 500 gal of brine with 35 lb of
of 7 gal /s. The mixture in tank 2 flows away at
salt, and tank 3 is empty. Suppose the mixture
the rate of 28 gal /s. How much salt is there in
flows out of tank 1 into tank 2 at the rate of 8
each tank as a function of time?
gal/ min and the mixture flows out tank 2 into
tank 3 at the rate of 22 gal /min. How much
10. Consider two tanks. Initially, tank 1 contains
salt is there in each tank as a function of time?
100 gal of brine (salt water) with 35 lb of salt,
13. Consider three tanks. Initially, tank 1 contains
and tank 2 contains 400 gal of brine with 15 lb
100 gal of brine (salt water) with 17 lb of salt,
of salt. Suppose the mixture flows out of tank 1
tank 2 contains 200 gal of brine with 19 lb of
into tank 2 at the rate of 17 gal/ min and the
salt, and tank 3 contains 300 gal of brine with
mixture flows out of tank 2 into tank I at the
21 lb of salt. Brine containing 5 lb of salt per
rate of 6 gal/ min. How much salt is there in
gallon enters tank 1 at the rate of 11 gal/s.
each tank as a function of time?
Mixed brine in tank 1 flows out into tank 2 at
11. Consider two tanks. Initially, tank 1 contains
the rate of 18 gal/s and the mixture also flows
out of tank 2 into tank 3 at the rate of 18
230 gal of brine (salt water) with 28 lb of salt,
gal/s. How much salt is there in each tank as a
and tank 2 contains 275 gal of brine with 7 lb
function of time?
of salt. Brine containing 5 1b of salt per gallon
enters tank 1 at the rate of 21 gal/s. Mixed
14. A large tank contains 7 gal of pure water.
brine in tank 1 flows out at the rate of 18
Polluted water containing 7 g of bacteria per
gal/s, half flowing into tank 2. The mixture in
gallon enters at the rate of 14 gal/h. A well-
tank 2 flows away at the rate of 4 gal/s. How
mixed mixture is removed at the rate of 4
much salt is there in each tank as a function of
gal/h. However, it is also known that the bac-
teria multiply inside the tank at a growth rate
time?
of 2% per hour. Determine the amount of
12. Consider three tanks. Initially, tank 1 contains
bacteria in the tank as a function of time.
1.10
Electronic Circuits
One of the applications of differential equations that will frequently recur
throughout this book is the theory of electronic circuits. There are several
reasons for this, among them the importance of circuit theory and the
pervasiveness of differential equations in circuit theory. (One of the authors
received his first exposure to circuit theory from a highly mathematical
electrical engineering professor by the name of Amar Bose. You would be
correct if you recognized the significance of his last name.) Also, circuits are
one example of what could be called network models. Network models are
widely used, for example, in manufacturing and other economic systems.
Circuits will be covered again in greater detail later. In this section we
shall introduce the basic circuit concepts we shall use and give some simple
examples of circuits that are described by first-order differential equations.
We consider only lumped-parameter circuits. In circuit theory, the word
circuit means that quantities such as current are determined solely by...

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- Fall '10
- capretta