
1.1. Equations of the Form f(x, y)
∂w
∂x
+ g(x, y)
∂w
∂y
= 0 23
3.
∂w
∂x
+
ae
λy
+ b
∂w
∂y
= 0.
Principal integral: Ξ = λ(bx −y) + ln
b + ae
λy
.
4.
∂w
∂x
+
ae
λy+βx
+ b
∂w
∂y
= 0.
Principal integral: Ξ = e
bλx−λy
+
aλ
β + bλ
e
(β+bλ)x
.
5.
∂w
∂x
+
ae
λy+βx
+ be
γx
∂w
∂y
= 0.
Principal integral: Ξ = e
−λy
E + aλ
Z
e
βx
E dx, where E = exp
bλ
γ
e
γx
.
6. ae
λx
∂w
∂x
+ be
βy
∂w
∂y
= 0.
Principal integral: Ξ =
1
βb
e
−βy
−
1
λa
e
−λx
.
7.
ae
λx
+ b
∂w
∂x
+
ce
βx
+ d
∂w
∂y
= 0.
Principal integral: Ξ = y −
Z
ce
βx
+ d
ae
λx
+ b
dx.
8.
ae
λx
+ b
∂w
∂x
+
ce
βy
+ d
∂w
∂y
= 0.
Principal integral: Ξ = λβ(dx − by) −dβ ln
ae
λx
+ b
+ bλ ln
ce
βy
+ d
.
9.
ae
λy
+ b
∂w
∂x
+
ce
βx
+ d
∂w
∂y
= 0.
Principal integral: Ξ = βλ(dx − by) + cλe
βx
− aβ ...