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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
Partial Diff erential Equations 8-31
From the first and last ratios
dx dz
xz
=
, cancelling (1 xy).
Integrating
11
log log log
x
xzc c
z
=+ ⇒= (8.193)
On cross-multiplication the first two ratios yield
22
22
22
, on transposition
() 1
, multiplying by
() ()
y dx xy dx x dy x y dy
x y dy xy dx y dx x dy
dy dx d xy
y x xy xy
−− =
⇒−=+
⇒−=
On integration we get
2
1
log log constant
1
log
yx
xy
y
c
xy x
−=−+
⎛⎞
+=
⎜⎟
⎝⎠
(8.194)
General solution is
1
, log 0
xy
F
zxy x
⎛⎞
⎛⎞
+=
⎜⎟
⎜⎟
⎝⎠
⎝⎠
(8.195)
Example 8.10.13 Solv
e (x
2
y
2
z
2
)p + 2xyq = 2xz.
[Bangalore 1990, Gorakhpur 1991, Andhra 1989]
Solution Lagrange’s auxiliary equations are
222
22
dx dy dz
xyz xy xz
==
−−
(8.196)
Considering ...
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Publisher Resources

ISBN: 9781299487406Publisher Website