
2.2. Equations of the Form f
1
∂w
∂x
+ f
2
∂w
∂y
+ f
3
∂w
∂z
= f
4
, f
n
= f
n
(x, y, z) 189
2. a
1
∂w
∂x
+a
2
∂w
∂y
+a
3
∂w
∂z
= b
1
arcsin(λ
1
x)+b
2
arcsin(λ
2
y)+b
3
arcsin(λ
3
z).
This is a special case of equation 2.2.7.10 with f (x) = a
1
, g(y) = a
2
, h(z) = a
3
, ϕ(x) =
b
1
arcsin(λ
1
x), ψ(y) = b
2
arcsin(λ
2
y), and χ(z) = b
3
arcsin(λ
3
z).
3. a
∂w
∂x
+ b
∂w
∂y
+ c arcsin
n
(λx) arcsin
k
(βz)
∂w
∂z
= s arcsin
m
(γx).
This is a special case of equation 2.2.7.12 with f
1
(x) = a, f
2
(x) = b, f
3
(x) = c arcsin
n
(λx),
f
4
(x) = s arcsin
m
(γx), g(y) = 1, and h(z) = arcsin
k
(βz).
4. a
∂w
∂x
+ b
∂w
∂y
+ c arcsin
n
(λx) arcsin
m
(βy) arcsin
k
(γz)
∂w
∂z
= s.
This is a special case of equation 2.2.7.19 with f (x, y) = c arcsin
n
(λx) arcsin
m
(