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Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
174 FIRST-ORDER EQUATIONS WITH THREE OR MORE INDEPENDENT VARIABLES
17. ax
2
∂w
∂x
+ by
2
∂w
∂y
+ cz
2
∂w
∂z
= kxy.
General solution: w =
kxy
ax by
ln
ax
y
+ Φ
b
x
a
y
,
c
x
a
z
.
18. ax
2
∂w
∂x
+ by
2
∂w
∂y
+ cz
2
∂w
∂z
= αx
2
+ βy
2
+ γz
2
.
General solution: w =
α
a
x +
β
b
y +
γ
c
z + Φ
b
x
a
y
,
c
x
a
z
.
Coefficients of equations contain other p owers in x, y, and z.
19.
∂w
∂x
+ a
∂w
∂y
+ b
∂w
∂z
= xyz.
General solution: w =
1
2
x
2
yz
1
6
x
3
(az + by) +
1
12
abx
4
+ Φ(y ax, z bx).
20. a
∂w
∂x
+ b
∂w
∂y
+ c
∂w
∂z
= kx
3
+ sy
2
.
General solution: w =
k
4a
x
4
+
s
3a
y
3
+ Φ(bx ay, cx az).
21. a
∂w
∂x
+ by
∂w
∂y
+ cz
∂w
∂z
= kx + s
x.
General solution: w =
k
2a
x
2
+
2s
3a
x
3/2
+ Φ
|y|
a
e
bx
, |z|
a
e
cx
.
22.
∂w
∂x
+ az
∂w
∂y
+ by
∂w
∂z
= c
x + s.
General soluti ...
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Publisher Resources

ISBN: 9781466581494