
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 ...