
164 FIRST-ORDER EQUATIONS WITH THREE OR MORE INDEPENDENT VARIABLES
14. a
∂w
∂x
+ b arctan
n
(λx)
∂w
∂y
+ c arctan
k
(βz)
∂w
∂z
= 0.
This is a special case of equation 2.1.7.16 with f
1
(x) = a, f
2
(x) = b arctan
n
(λx), f
3
(x) = 1,
g(y) = 1, and h(z) = c arctan
k
(βz).
15. a
∂w
∂x
+ b arctan
n
(λy)
∂w
∂y
+ c arctan
k
(βz)
∂w
∂z
= 0.
This is a special case of equation 2.1.7.15 with f(x) = a, g(y) = b arctan
n
(λy), and
h(z) = c arctan
k
(βz).
◮ Coefficients of equations contain arccotangent.
16. a
∂w
∂x
+ b
∂w
∂y
+ c arccot
n
(λx) arccot
k
(βz)
∂w
∂z
= 0.
This is a special case of equation 2.1.7.16 with f
1
(x) = a, f
2
(x) = b, f
3
(x) = c arccot
n
(λx),
g(y) = 1, and h(z) = arccot
k
(βz).
17. a
∂w
∂x
+ b
∂w
∂y
+ c ar ...