Differential Equations - 3 - PowerPoint PPT Presentation

1 / 25
About This Presentation
Title:

Differential Equations - 3

Description:

Mathematics * * * * * * * * * * * * * * * * * * Session Differential Equations - 3 Session Objectives Linear Differential Equations Differential Equations of Second ... – PowerPoint PPT presentation

Number of Views:299
Avg rating:3.0/5.0
Slides: 26
Provided by: mediaCaree2
Category:

less

Transcript and Presenter's Notes

Title: Differential Equations - 3


1
(No Transcript)
2
Session
Differential Equations - 3
3
Session Objectives
  • Linear Differential Equations
  • Applications of Differential Equations
  • Differential Equations of Second Order
  • Class Exercise

4
Linear Differential Equations
5
Linear Differential Equations type-1
where P and Q are the functions of x, or
constants.
6
Example 1
7
Solution Cont.
8
Example -2
Solution The given differential equation is
9
Solution Cont.
The solution is given by
10
Example 3
11
Solution Cont.
The solution is given by
12
Linear Differential Equations type 2
where P and Q are the functions of y, or
constants.
13
Example - 4
Solution The given differential equation is
14
Solution Cont.
The solution is given by
15
Applications of Differential Equations
Differential equations are used to solve problems
of science and engineering.
16
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
17
Solution Cont.
At t 0, P P0
18
Example - 6
19
Solution Cont.
The curve passes through the point (3, 4).
20
Differential Equations of Second Order
is the required general solution of the given
differential equation.
21
Example -7
Solution The given differential equation is
22
Solution Cont.
23
Example 8
Integrating (i), we get
24
Solution Cont.
Again integrating both sides of (ii), we get
25
(No Transcript)
Write a Comment
User Comments (0)
About PowerShow.com