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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
88 FIRST-ORDER EQUATIONS WITH TWO INDEPENDENT VARIABLES
20. f (x)
∂w
∂x
+ g(y)
∂w
∂y
= h
1
(x) + h
2
(y).
General solution:
w =
Z
h
1
(x)
f(x)
dx +
Z
h
2
(y)
g(y)
dy + Φ
Z
dx
f(x)
Z
dy
g(y)
.
21. f
1
(x)
∂w
∂x
+

f
2
(x)y + f
3
(x)y
k

∂w
∂y
= g(x)h(y).
The transformation ξ =
Z
f
2
(x)
f
1
(x)
dx, η = y
1k
leads to an equation of the form 1.2.7.19:
∂w
∂ξ
+
(1 k)η + F (ξ)
∂w
∂η
= G(ξ)H(η),
where F (ξ) = (1 k)
f
3
(x)
f
2
(x)
, G(ξ) =
g(x)
f
2
(x)
, and H(η) = h(y).
22. f
1
(x)g
1
(y)
∂w
∂x
+ f
2
(x)g
2
(y)
∂w
∂y
= h
1
(x)h
2
(y).
The transformation ξ =
Z
f
2
(x)
f
1
(x)
dx, η =
Z
g
1
(y)
g
2
(y)
dy leads to an equation of the form
1.2.7.18:
∂w
∂ξ
+
∂w
∂η
= F (ξ)G(η), where F (ξ) =
h
1
(x)
f
2
(x)
, G(η) =
h
2
(y)
g
1
(y)
.
23. f
1
(x)g
1
(y)
∂w
∂x
+ f
2
(x)g
2
(y)
∂w
∂y
= h
1
(
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Publisher Resources

ISBN: 9781466581494