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Unformatted text preview: e. The set of ODEs is du
=x
dt dx
=x
dt The solution of the ﬁrst is
ln x = ln x0 + t
or
x = x0 et
Now substitute x in the second ODE
du
= x0 et
dt
and integrate it
u(x, t) = et x0 + K
At t = 0 the solution is
u(x0 , 0) = f (x0 ) = K + x0 plug t = 0 in the solution u Thus when substituting K in u
u(x, t) = x0 et + f (x0 ) − x0
Now substitute for x0 in the solution
u(x, t) = x + f x e−t − x e−t 253 ...
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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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