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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 5-25
11.
2
2584
2
44(64)0.
dy dy
xxxxy
dx dx
++++=
Ans:
4
8
3
sin log 4
2
x
yce x x
⎛⎞
=+
⎜⎟
⎝⎠
12.
2
2
2tan 5 sec .
x
dy dy
xyxe
dx dx
−+=
Ans:
12
1
(sin6 cos6)sec sec
7
x
yc xc x x e x=+ +
5.3 GENERAL SOLUTION OF
2
2
dy dy
PQyR
dx dx
+=
+ =
BY CHANGING THE INDEPENDENT VARIABLE
The differential equation is
2
2
dy dy
PQyR
dx dx
++= (5.40)
Let the independent variable x be changed to z
where ().zzx=
We have
2
22 2
22 2
and
dy dy dz d y d y dz dy d z
dx dz dx dx dz dx dz dx
⎛⎞
==+
⎜⎟
⎝⎠
Substituting in (5.40)
2
22
22
dz d y dy d z dy dz
PQyR
dx dx dx dx dz dx
⎛⎞
++ +=
⎜⎟
⎝⎠
2
22
22
dz d y d z dz dy
PQyR
dx dz dx dx dz
⎛⎞
⎛⎞
++ +=
⎜⎟
⎜⎟
⎝⎠
⎝⎠
Dividing by
2
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Publisher Resources

ISBN: 9781299487406Publisher Website