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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
3.8. Equations Containing Arbitrary Functions 381
3
. The structure of particular solutions ¯w(x, t) of the nonhomogeneous equation 3.8.6.5
for some functions Φ(x, t) is presented in Table 3.4.
Remark 3.7. The homogene ous equation (with Φ 0) admits all the particular solutions spec-
ified in Table 3.4. In this case, n should be assumed a n integer an d β and λ arbitrary nu mbers.
TABLE 3.4
Structure of particular solutions of linear nonhomogeneous equations of special form
No Functions Φ(x, t) Form of particular solutions ¯w(x, t) Remarks
1
ϕ(x)t
n
n
P
m=0
ψ
m
(x)t
m
n is an integer; the equations
for ψ
m
(x) are solved consecutively,
starting with m = n
2
ϕ(x)
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Publisher Resources

ISBN: 9781466581494