APPLICATIONS OF FIRST ORDER DIFFERENTIAL EQUATION

1. APPLICATIONS
OF FIRST ORDER
DIFFERENTIAL
EQUATION

2. 1storderdifferentialequation:
‐ Definition of 1st order differential equation:
1st order differential equation is one kind of
differential equation.
A differential equation involving derivatives of one or
more dependent variables with respect to a single
independent variable and which has only one order
derivatives, is called a 1st order differential equation.
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3. 1storderdifferentialequation:
‐ Example:
is a 1st order differential equation. Here y is a
dependent variable and x is a independent variable
and 𝑑 /𝑑𝑥 is the derivative term which order is one,
so it is a 1st order differential equation.
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4. 1storderdifferentialequation:
Standard form of 1st order ordinary
differential equation:
The standard form of 1st order ordinary
differential equation is
𝑑𝑦 /𝑑𝑥 = 𝑓( 𝑥, 𝑦) ⋯ ⋯ ⋯ ⋯ ⋯ 1
or the differential form
𝑀 (𝑥, 𝑦) 𝑑𝑥 + 𝑁 (𝑥, 𝑦) 𝑑𝑦 = 0 ⋯ ⋯ ⋯ 2
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5. APPLICATIONS OF
FIRST ORDER
DIFFERENTIAL
EQUATION

6. There are a lot of applications of 1st order
ordinary differential equation in our
real life in various sectors.
Some of these are given below:
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 Cooling/Warming Law (use in physics)
 Population Growth and Decay (in stat..)
 Radio-Active Decay and Carbon Dating
 Mixture of Two Salt Solutions(in chemistry)
 Series Circuits (in physics)
 Survivability with AIDS (in medicine)
APPLICATIONS OF FIRST ORDER DIFFERENTIAL EQUATION

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APPLICATIONS OF FIRST ORDER DIFFERENTIAL EQUATION
 Draining a tank (in engineering)
 Determining the motion of a projectile, rocket, satellite
or planet (in engineering).
 Determining the charge or current in a electric Group D
 Determination of curves that have certain geometrical
properties.
And so on…

9. Applicationsof1st order
differentialequation:
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Lets see some applications of 1st order
differential equation with example.

10. physics)
‐ Newton's law of cooling states that the rate of
change of temperature is proportional to the
difference between the temperature of body and
its surroundings.
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Problem: Suppose, at 10:00am you took a cup of hot
instant coffee from your microwave oven and placed it in a
nearby kitchen counter to cool. At this instant, the temperature
of the coffee is 180℉ and 10 minutes later it was 160℉.
Assume that the constant temperature of the kitchen was 70℉.
What was the temperature of the coffee at 10:15 am?
1.Cooling/Warming Law (use in physics)

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1.Cooling/Warming Law (use in physics)
Let 𝑦(𝑡) is the temperature of the coffee after t min and 𝑦𝑠
the temp of kitchen. According to Newton’s Law of cooling

13. 1.Cooling/Warming Law (use in
physics)
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1.Cooling/Warming Law (use in physics)

15. 2. Population Growth and Decay (in statistics)
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Problem: A population grows at the rate of 5% per
year. How long does it takes for the population to
double?
Solution: Let the initial population be and let the
population after t years be p. Then we get

16. Decay (in statistics)
which is a separable differential equation. Now we
integrating (1) and we get,
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2. Population Growth and Decay (in statistics)

18. 2. Population Growth and Decay (in
statistics)
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19. 3. Determination of curves that
have certain geometrical
properties.
‐ Problem: The slope of the tangent at a point (x, y) on a
curve is (− 𝑥 /𝑦 ). If the curve passes through the point
(3,-4). Find the equation of the curve.
Solution: We know the slope of a curve at point (x, y)
is
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20. have certain geometrical
properties
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21. 3. Determination of curves that
have certain geometrical
properties
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3. Determination of curves that have certain
geometrical properties

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4.Carbon Dating
Problem: Find the age of an object that has been excavated and
found to have 90% of its original amount of radioactive Carbon 14.

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4.Carbon Dating

25. 5.Radioactive Material
‐ Problem: A radio active material has an initial mass
100mg. After two years it is left to 75mg. Find the
amount of the material at any time. What is the
period of its half-life?
‐ Solution: We measure the amount of the material
present at any time t. We have
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5.Radioactive Material

27. 5.Radioactive Material
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28. 5.Radioactive Material
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29. 6.Electrical Circuit (use in physics)
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Problem: A battery giving a constant voltage of E(t) = 40V is
connected in series to a resistor of resistance 20Ω and an
inductor of inductance 1H. If the initial current in the circuit is
i(0) = 3A, and the current after t seconds.

30. 6.Electrical Circuit (use in
physics)
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