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Wednesday, January 25
−
Lecture 12 :
Secondorder Differential equations
.
(Not
explicitly discussed in your text)
After having practiced the problems associated to the concepts of this lecture the student should
be able to
:
Solve secondorder differential equations which can be reduced to a first order DE.
Normally these are second order DE’s where there is a variable missing.
12.1
Secondorder equations can always be expressed in the form
F
(
x
,
y
,
y
',
y
'') = 0.
There are two types of secondorder differential equations for which we have
relatively easy methods of solution. We study them below.
Remarks
In the examples below you will note that initial value problems for second order
differential equations have two initial conditions:
y
'(
a
) =
b
and
y
(
c
) =
d
.
Also note that in the following examples
v
=
v
(
x
) and
y
=
y
(
x
) and so
all their
derivatives are with respect to
x
.
12.1.1 Type I :
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This note was uploaded on 03/19/2012 for the course MATH 118 taught by Professor Zhou during the Winter '08 term at Waterloo.
 Winter '08
 ZHOU
 Differential Equations, Calculus, Equations

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