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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
23.2. Analytical Solutions and Their Visualizations 1337
Remark. The system of characteristic equation s dx/x = dy/y = du/u gives th e integral surfaces
(
eq11
,
eq21
):
φ =
y
x
= C
1
, ψ =
u
x
= C
2
,
where C
1
and C
2
are arbitrary constants. H ence, according to Eq. (23.2.2.3), the general solution of
the linear PDE is f (y/x, u/x) = 0 (
genSol
), where f is an arbitrary functio n. This solution can be
verified (
test1
). By applying the predefined function
DSolve
, we find the result in a different form:
u (x, y) = xg
y
x
.
This form of the general solution can be obtained (
genSol2
) and verified (
test2
).
Example 23.8. Linear Euler equation. Gene ral solution. By a pplying
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Publisher Resources

ISBN: 9781466581494