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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
8-26 Diff erential Equations
8.10.3 Method of Multipliers
In addition to the above methods, we can apply the following method
called method of multipliers.
Example 8.10.4 Solve x
2
(y z)p + y
2
(z x)q = z
2
(x y).
Solution Lagrange’s auxiliary equations are
222
()()()
dx dy dz
xyz yz x zx y
==
−−−
(8.158)
Using multipliers
111
,,
xyz
⎛⎞
⎜⎟
⎝⎠
and
222
111
,,
xyz
⎛⎞
⎜⎟
⎝⎠
in turn we get
222
111
1
1
111
222
2
each ratio
()()()0
0
log log log log
each ratio
()()()0
111
0
111
xyz
xyz
dx dy dz
xy z yz x zx y
dx dy dz
xyz
xyzc
xyz c
dx dy dz
yz zx xy
dx dy dz
xyz
c
xyz
++
=
−+ −+ −=
⇒++=
⇒++=
⇒=
++
=
−+−+−=
⇒++=
⇒++=
(8.159)
General solution is
111
,0F xyz
xyz
⎛⎞
++ =
⎜⎟
⎝⎠
(8.163)
Example 8.10.5 Solve zxp +
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Publisher Resources

ISBN: 9781299487406Publisher Website