PPT: First Order Differential Equations | Engineering Mathematics - Civil Engineering (CE) PDF Download

 Page 1


First Order Ordinary Linear 
Differential Equations
•
Ordinary Differential equations does not 
include partial derivatives.
•
A linear first order equation is an equation 
that can be expressed in the form
  
Where p and q are functions of x
Page 2


First Order Ordinary Linear 
Differential Equations
•
Ordinary Differential equations does not 
include partial derivatives.
•
A linear first order equation is an equation 
that can be expressed in the form
  
Where p and q are functions of x
Types Of Linear DE:
1. Separable Variable
2. Homogeneous Equation
3. Exact Equation
4. Linear Equation
Page 3


First Order Ordinary Linear 
Differential Equations
•
Ordinary Differential equations does not 
include partial derivatives.
•
A linear first order equation is an equation 
that can be expressed in the form
  
Where p and q are functions of x
Types Of Linear DE:
1. Separable Variable
2. Homogeneous Equation
3. Exact Equation
4. Linear Equation
The first-order differential equation 
( )
,
dy
f x y
dx
=
is called separable provided that f(x,y) 
can be written as the product of a 
function of x and a function of y. 
(1)
Separable Variable
Page 4


First Order Ordinary Linear 
Differential Equations
•
Ordinary Differential equations does not 
include partial derivatives.
•
A linear first order equation is an equation 
that can be expressed in the form
  
Where p and q are functions of x
Types Of Linear DE:
1. Separable Variable
2. Homogeneous Equation
3. Exact Equation
4. Linear Equation
The first-order differential equation 
( )
,
dy
f x y
dx
=
is called separable provided that f(x,y) 
can be written as the product of a 
function of x and a function of y. 
(1)
Separable Variable
Suppose we can write the above equation as 
) ( ) ( y h x g
dx
dy
=
We then say we have “ separated ” the 
variables. By taking h(y) to the LHS, the 
equation becomes
Page 5


First Order Ordinary Linear 
Differential Equations
•
Ordinary Differential equations does not 
include partial derivatives.
•
A linear first order equation is an equation 
that can be expressed in the form
  
Where p and q are functions of x
Types Of Linear DE:
1. Separable Variable
2. Homogeneous Equation
3. Exact Equation
4. Linear Equation
The first-order differential equation 
( )
,
dy
f x y
dx
=
is called separable provided that f(x,y) 
can be written as the product of a 
function of x and a function of y. 
(1)
Separable Variable
Suppose we can write the above equation as 
) ( ) ( y h x g
dx
dy
=
We then say we have “ separated ” the 
variables. By taking h(y) to the LHS, the 
equation becomes
1
( )
( )
dy g x dx
h y
=
Integrating, we get the solution as
1
( )
( )
dy g x dx c
h y
= +
? ?
where c is an arbitrary constant.