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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
2.4. Equations of the Form f
1
∂w
∂x
+ f
2
∂w
∂y
+ f
3
∂w
∂z
= f
4
w + f
5
, f
n
= f
n
(x, y, z) 249
1
. Any two out of three functions u, v, and w can be assumed to be arbitrary, and the
remaining function is determined by a simple single integration of Eq. (1).
This method permits one to obtain the general solution in the form
u = u(x, y, z) is an arbitrary function,
v = v(x, y, z) is an arbitrary function,
w =
Z
(u
x
+ v
y
) dz + ξ
3
(x, y).
2
. Suppose that ψ
(1)
= ψ
(1)
(x, y, z) and ψ
(1)
= ψ
(2)
(x, y, z) are two arbitrary twice
continuously differentiable functions.
2.1. The general solution of Eq. (1) can be represented, for example, in the simple form
u = (u, v, w), u = ψ
(1) ...
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Publisher Resources

ISBN: 9781466581494