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Unformatted text preview: 3. The ODEs in this case are dx
= 2u
dt
du
=0
dt
Since the ﬁrst ODE contains x, t and u, we solve the second ODE ﬁrst
u(x, t) = u(x(0), 0) = f (x(0))
Plug this u in the ﬁrst ODE, we get
dx
= 2f (x(0))
dt
The solution is
x = x0 + 2tf (x0 )
These are characteristics lines all with slope
1
2f (x0 )
Note that the characteristic through x1 (0) will have a diﬀerent slope than the one through
x2 (0). That is the straight line are NOT parallel. 236 ...
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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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