u
ξη
=
1
3
u
η
−
8
9
This equation can be solved as follows:
Let
ν
=
u
η
then
u
ξη
=
ν
ξ
ν
ξ
=
1
3
ν
−
8
9
This is Linear 1
st
order ODE
ν
0
−
1
3
ν
=
−
8
9
Integrating factor is
e
−
1
3
ξ
(
νe
−
1
3
ξ
)
0
=
−
8
9
e
−
1
3
ξ
νe
−
1
3
ξ
=
−
8
9
Z
e
−
1
3
ξ
d
ξ
=
8
3
e
−
1
3
ξ
+
C
(
η
)
ν
=
8
3
+
C
(
η
)
e
1
3
ξ
To Fnd
u
we integrate with respect to
η
u
η
=
8
3
+
C
(
η
)
e
1
3
ξ
u
=
8
3
η
+
e
1
3
ξ
c
1
(
η
)

{z
}
integral of
C
(
η
)
+
K
(
ξ
)
To check the solution, we di±erentiate it and substitute in the canonical form:
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.
 Fall '08
 BELL,D

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