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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
1128 METHODS FOR FIRST-ORDER LINEAR PDES
Equation (13.1.2.5) can be treated as an ordinary differential equation for w = w(x)
with parameter u. The general solution of Eq. (13.1.2.5) has the form
w = E
Z
¯
h
0
(x, u)
¯
f(x, u)
dx
E
+ Φ(u)
, E = exp
Z
¯
h
1
(x, u)
¯
f(x, u)
dx
,
where Φ is an arbitrary function; in the integration, u is considered a parameter. To find a
general integral of Eq. (13.1.2.1), one should compute the integrals in the last relation and
then return to the original variables x and y.
Classical and generalized C auchy problems. Solution methods.
1
. The classical and generalized Cauchy problems for Eq. (13.1.2.1) are stated in the same
manner ...
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Publisher Resources

ISBN: 9781466581494