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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
8-18 Diff erential Equations
8.7.3 Particular Integral
When a particular function f is used in (8.101) we obtain a particu-
lar integral or particular solution of the partial differential equation
(8.93).
8.7.4 Singular Integral
In some cases we fi nd another integral which satisfi es the partial dif-
ferential equation (8.93) but is not a particular integral of (8.93). If it
exists, it is obtained by eliminating a and b from
( , , , ), 0 and 0
FF
zFxyab
ab
∂∂
===
∂∂
(8.102), (8.103), (8.104)
and it is the envelope of the two-parameter family of surf
aces
z = F(x, y, a, b) (8.105)
and it is called a singular integral (or a singular solution).
In a sense, a general ...
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Publisher Resources

ISBN: 9781299487406Publisher Website