
1.1. Equations of the Form f(x, y)
∂w
∂x
+ g(x, y)
∂w
∂y
= 0 13
65.
∂w
∂x
+ (ax
n
y
2
+ bx
m
y + bcx
m
− ac
2
x
n
)
∂w
∂y
= 0.
1
◦
. Principal integral for m, n 6= −1:
Ξ =
E
y + c
+ a
Z
x
n
E dx, E = exp
b
m + 1
x
m+1
−
2ac
n + 1
x
n+1
.
2
◦
. Principal integral for n = −1:
Ξ =
x
−2ac
y + c
exp
b
m + 1
x
m+1
+ a
Z
x
−2ac−1
exp
b
m + 1
x
m+1
dx.
3
◦
. Principal integral for m = −1:
Ξ =
x
b
y + c
exp
−
2ac
n + 1
x
n+1
+ a
Z
x
n+b
exp
−
2ac
n + 1
x
n+1
dx.
66.
∂w
∂x
+
ax
n
y
2
− ax
n
(bx
m
+ c)y + bmx
m−1
∂w
∂y
= 0.
1
◦
. Principal integral for n 6= −1 and m + n 6= −1:
Ξ =
E
y − bx
m
− c
+ a
Z
x
n
E dx, E = exp
abx
n+m+1
n + m + 1
+
acx
n+1
n + 1
.
2
◦
. Principal integral for n = −1 and m 6= 0:
Ξ =
x
ac
y − bx
m
− c
exp
ab
m
x
m
+ a
Z
x
ac−1
exp
ab
m
x
m
dx.
3
◦
. Principal integ ...