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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
Chapter 2
First-Order Equations with Three
or More Independent Variables
2.1 Equations of the Form
f(x, y, z)
∂w
∂x
+ g(x, y, z)
∂w
∂y
+ h(x, y, z)
∂w
∂z
= 0
For brevity, only an
integral basis
u
1
= u
1
(x, y), u
2
= u
2
(x, y)
of an equation will often be presented in Section 2.1. The general solution of the equation
is given by
w = Φ(u
1
, u
2
),
where
Φ = Φ(u
1
, u
2
)
is an arbitrary function of two variables.
2.1.1 Equations Containing Power-Law Functions
Coefficients of equations are linear in x, y, and z.
1. a
∂w
∂x
+ b
∂w
∂y
+ c
∂w
∂z
= 0.
Integral basis: u
1
= bx ay, u
2
= cx az.
Literature: E. Kamke (1965).
2.
∂w
∂x
+ ax
∂w
∂y
+ by
∂w
∂z
= 0.
Integral basis: u
1
= ax
2
2y, u
2
= 3z + bx(ax
2
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Publisher Resources

ISBN: 9781466581494