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Differential Equations - 3

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Title: Differential Equations - 3


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Session
Differential Equations - 3
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Session Objectives
  • Linear Differential Equations
  • Applications of Differential Equations
  • Differential Equations of Second Order
  • Class Exercise

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Linear Differential Equations
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Linear Differential Equations type-1
where P and Q are the functions of x, or
constants.
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Example 1
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Solution Cont.
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Example -2
Solution The given differential equation is
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Solution Cont.
The solution is given by
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Example 3
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Solution Cont.
The solution is given by
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Linear Differential Equations type 2
where P and Q are the functions of y, or
constants.
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Example - 4
Solution The given differential equation is
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Solution Cont.
The solution is given by
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Applications of Differential Equations
Differential equations are used to solve problems
of science and engineering.
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Example - 5
A population grows at the rate of 5 per year.
How long does it take for the population to
double? Use differential equation for it.
Solution Let the initial population be P0 and
let the population after t years
be P, then
Integrating both sides
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Solution Cont.
At t 0, P P0
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Example - 6
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Solution Cont.
The curve passes through the point (3, 4).
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Differential Equations of Second Order
is the required general solution of the given
differential equation.
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Example -7
Solution The given differential equation is
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Solution Cont.
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Example 8
Integrating (i), we get
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Solution Cont.
Again integrating both sides of (ii), we get
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