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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
9.4. Other Equations 851
where Φ(x) and Ψ(y) are determined by the following second-order linear ordinary differ-
ential equations (C is an arbitrary constant):
(fΦ
x
)
x
βΦ = C, f = f(x),
(gΨ
y
)
y
βΨ = C, g = g(y).
In the special case β = 0, the solutions of these equations can be represented as
Φ(x) = C
Z
x dx
f(x)
+ A
1
Z
dx
f(x)
+ B
1
,
Ψ(y) = C
Z
y dy
g(y)
+ A
2
Z
dy
g(y)
+ B
2
,
where A
1
, A
2
, B
1
, and B
2
are arbitrary constants.
9.4.4 Other Equations Arising in App lications
1. y
2
w
∂x
2
+
2
w
∂y
2
= 0.
Tricomi equation. It is used to describe near-sonic flows of gas.
1
. Particular solutions:
w = Axy + Bx + Cy + D,
w = A(3x
2
y
3
) + B(x
3
xy
3
) + C(6yx
2
y
4
),
where A, B, C, and
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Publisher Resources

ISBN: 9781466581494