
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