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Differential Equations by Pearson
book

Differential Equations by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
472 pages
13h 25m
English
Pearson India
Content preview from Differential Equations by Pearson
Linear Equation of the Second Order with Variable Coeffi cients 5-13
which is a linear equation in p. The integrating factor is
2
11
2log
2log
2
1
dx
x
xx
eee
x
===
Its solution is
1
22
112
1
x
p e dx c
xx x
⎛⎞
=− +
⎜⎟
⎝⎠
()
23
1
2
xx
x e x e dx c
−−
=− +
(
)
(
)
(
)
2
1
xx x
x e c e f x f x dx e f x
=+∴ + =
⎡⎤
⎣⎦
1
x
dv
pecx
dx
==+
Integrating
3
12
3
x
x
ve c c
⎛⎞
=+ +
⎜⎟
⎝⎠
The general solution of (5.12) is
3
2
12
3
xxxx
x
yvec ecee== + +
Example 5.1.11 Solve
2
2
2
(2) 2 .
dy dy
xx yx
dx dx
−−=
Solution Dividing by x, the giv
en equation in the standard form is
2
2
2
22
1
dy dy
yx
dx x dx x
⎛⎞
+− =
⎜⎟
⎝⎠
(5.16)
where
2
22
1, ,PQRx
xx
=− =− =
Since
22
1110PQ
xx
−+=−+−=
x
ye
=
is a part of the C. F. of (5.16)
Let
x
yve
=
, where
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Publisher Resources

ISBN: 9781299487406Publisher Website