
214 FIRST-ORDER EQUATIONS WITH THREE OR MORE INDEPENDENT VARIABLES
25.
∂w
∂x
+ a cos
n
(λx)
∂w
∂y
+ b tan
m
(βy)
∂w
∂z
=
c cos
k
(γy) + s tan
l
(µz)
w.
This is a special case of equation 2.3.7.22 with f
1
(x) = 0, f
2
(x) = a cos
n
(λx), g
1
(x, y) = 0,
g
2
(x, y) = b tan
m
(βy), and h(x, y, z) = c cos
k
(γy) + s tan
l
(µz).
26. a
1
sin
n
1
(λ
1
x)
∂w
∂x
+ b
1
cos
m
1
(β
1
y)
∂w
∂y
+ c
1
cos
k
1
(γ
1
z)
∂w
∂z
=
a
2
cos
n
2
(λ
2
x) + b
2
sin
m
2
(β
2
y) + c
2
cos
k
2
(γ
2
z)
w.
This is a special case of equation 2.3.7.10 with f (x)=a
1
sin
n
1
(λ
1
x), g(y)=b
1
cos
m
1
(β
1
y),
h(z) = c
1
cos
k
1
(γ
1
z), ϕ(x) = a
2
cos
n
2
(λ
2
x), ψ(y) = b
2
sin
m
2
(β
2
y), χ(z) = c
2
cos
k
2
(γ
2
z).
27. a
1
tan
n
1
(λ
1
x)
∂w
∂x
+ b
1
cot
m
1
(β
1
y)
∂w
∂y
+ c
1
cot
k
1
(γ
1
z)
∂w
∂z
=
a
2
cot
n
2
(λ
2
x) + b
2
tan
m