
8-38 Diff erential Equations
14. p tan x + q tan y = tan z. [Andhra 1990, Kerala 1987 S]
Ans:
sin sin
,0
sin sin
xx
F
yz
⎛⎞
=
⎜⎟
⎝⎠
15. xe
y
p + (1 − e
y
)q = ze
y
.
Ans:
,( )(1 ) 0
y
x
Fxze
z
⎛⎞
+− =
⎜⎟
⎝⎠
8.11 NONLINEAR EQUATIONS OF FIRST ORDER
The most general partial differential equation of the first order in two
independent variables is of the form
f (x, y, z, p, q) = 0 (8.231)
which may not be linear.
We do not propose to study any general method of integration of
Eq. (8.231) but consider only four standard forms which admit inte-
gration by very short processes. Also, many equations can be reduced
to one or the other of these four forms.
The general integral, ...