
1.2. Equations of the Form f(x, y)
∂w
∂x
+ g(x, y)
∂w
∂y
= h(x, y) 73
10. ae
βx
∂w
∂x
+ be
γx+λy
∂w
∂y
= ce
µx+δy
+ k.
This is a special case of equation 1.2.7.37 with f (x) = ae
βx
, g
1
(x) ≡ 0, g
0
(x) = be
γx
, and
h(x, y) = ce
µx+δy
+ k.
11. ae
λy
∂w
∂x
+ be
βx
∂w
∂y
= ce
γx
+ d.
This is a special case of equation 1.2.7.16 with f (x) = a, g(x) = be
βx
, and h(x) = ce
γx
+d.
◮ Coefficients of equations contain exponential and power-law functions.
12. a
∂w
∂x
+ b
∂w
∂y
= cye
λx
+ kxe
µy
.
General solution: w =
c
aλ
e
λx
y −
b
aλ
+
k
bµ
e
µy
x −
a
bµ
+ Φ(bx − ay).
13.
∂w
∂x
+ a
∂w
∂y
= ax
k
e
λy
.
This is a special case of equation 1.2.7.5 with f (x) = ax
k
.
14.
∂w
∂x
+ (ay + be
λx
)
∂w
∂y
= ce
βx
.
This is a special case of equation ...