LECTURE # 18
Article 29
Gauss Hyper geometric Equation
Gauss Hyper geometric Equation
The equation is :
x(1 x ) y + [c (a + b + 1)x] y aby = 0
where a, b, c are constants.
(1)
Here ,
c (a + b + 1)x
a
Lecture #14
Series Solution of First O.D.E
Section 27
Series Solution of First Order D.E.
(1)In each of following D.E. find a power series
an x n , try to recognize the
solution of the form
resulting
Section 26
Review of Power series
Lecture # 13
Review of Power Series
An infinite series of the form
an x n = a0 + a1 x + a2 x 2 + .
(1)
n =0
is called a power series in x.
The series
a (x x )
n
n
0
LECTURE #12
The STURM Comparison Theorem
Section 25
The STURM Comparison Theorem
Theorem A :
Let
y(x )
be a non-trivial solution of
y + q( x ) y = 0
(1)
on a closed interval [a,b]. Then
y(x )
has
at
LECTURE # 10
Section 23
Operator methods for finding
particular solution
Section 23
Operator methods for finding particular solution
(a)
D
dy
d2y
dny
Dy = , D 2 y = 2 ,., D n y = n
dx
dx
dx
differenti
Lecture # 9
The method of variation of parameters
Section 19
The method of variation of parameters
Let
y + P( x ) y + Q(x ) y = R( x ) (1)
where
P(x ), Q( x ), R( x )
are function of x or const.
Let t
Lecture # 8
The Method of Undetermined Coefficients
Section 18
The Method of Undetermined Coefficients
Qn. 3)
If
y1 ( x) and y2 ( x) are solution of
y '+ P( x) y '+ Q( x) y = R1 ( x)
and y '+ P( x) y
LECTURE # 7
LECTURE
The use of a known solution to find
another
another
The Homogeneous Equation with
constant coefficient
constant
ARTICLE 16
ARTICLE
The use of known solution to find
The
another
ano
LECTURE #5,#6
Section 14-15
Introduction
The general solution of a Homogeneous
Equation
A second order linear diff eqn. (lde) is eqn. of the
second
of
form
form
a0(x)y + a1(x)y + a2(x)y = h(x)
where a
LECTURE # 4
Section 10 &11
Linear Equations
Reduction of Order
Section 10
Linear Equations
To solve the equation
dy
= 2 xy ( y > 0 )
dx
(1)
we multiply both sides by the factor 1/y to
get,
1 dy
.
= 2
LECTURE # III
Section 09
Integrating Factors
Section 09
Integrating Factors
Exact differential equations are comparatively rare,
for, exactness depend on a precise balance in the
form of the equation
LECTURE # II
Section 07 -08
Separable Equations and applications
Implicit solutions and General Solutions
Homogeneous Equations
Equations reducible to homogeneous form
Exact equations
Linear vs. Nonli
Differential Equations
MATH C241
Text Book: Differential Equations with
Applications and Historical Notes: George
F. Simmons, 2ed.,TMH
Lecture Notes prepared by:
Dr. Bimal Kumar Mishra
Mathematics Gro