
194 FIRST-ORDER EQUATIONS WITH THREE OR MORE INDEPENDENT VARIABLES
14.
∂w
∂x
+
f
1
(x)y + f
2
(x)y
k
∂w
∂y
+
g
1
(y)z + g
2
(x)z
m
∂w
∂z
= h
1
(x) + h
2
(y).
This is a special case of equation 2.2.7.23 with g
1
(x, y) = g
1
(y), g
2
(x, y) = g
2
(x), and
h(x, y, z) = h
1
(x) + h
2
(y).
15.
∂w
∂x
+
f
1
(x)y + f
2
(x)y
k
∂w
∂y
+
g
1
(x) + g
2
(y)e
λz
∂w
∂z
= h
1
(x) + h
2
(y).
This is a special case of equation 2.2.7.24 with g
1
(x, y) = g
1
(x), g
2
(x, y) = g
2
(y), and
h(x, y, z) = h
1
(x) + h
2
(y).
16.
∂w
∂x
+
f
1
(x) + f
2
(x)e
λy
∂w
∂y
+
g
1
(y)z + g
2
(x)z
k
∂w
∂z
= h
1
(x) + h
2
(y).
This is a special case of equation 2.2.7.25 with g
1
(x, y) = g
1
(y), g
2
(x, y) = g
2
(x), and
h(x, y, z) = h
1
(x) + h
2
(y).
17.
∂w
∂x
+
f
1
(x) +