
1.1. Equations of the Form f(x, y)
∂w
∂x
+ g(x, y)
∂w
∂y
= 0 43
49. cot(µy)
∂w
∂x
+ a cot(λx)
∂w
∂y
= 0.
Principal integral: Ξ = aµ ln
sin(λx)
− λ ln
sin(µy)
.
50. cot(µy)
∂w
∂x
+ a cot
2
(λx)
∂w
∂y
= 0.
Principal integral: Ξ = λ ln
sin(µy)
+ aµ cot(λx) + aλµx.
51. cot(y + a)
∂w
∂x
+ c cot(x + b)
∂w
∂y
= 0.
Principal integral: Ξ = c ln
sin(x + b)
− ln
sin(y + a)
.
52. cot(λx) cot(µy)
∂w
∂x
+ a
∂w
∂y
= 0.
Principal integral: Ξ = λ ln
sin(µy)
+ aµ ln
cos(λx)
.
53. cot(λx) cot(µy)
∂w
∂x
+ a cot(νx)
∂w
∂y
= 0.
Principal integral: Ξ = aµ
Z
cot(νx)
cot(λx)
dx − ln
sin(µy)
.
◮ Coefficients of equations contain different trigonometric fu nctions.
54.
∂w
∂x
+ a sin
k
(λx) cos
n
(µy)
∂w
∂y
= 0.
Principal ...