Unformatted text preview: 1.
a. Integrate the PDE assuming x ﬁxed, we get
u(x, t) = K (x)
Since dx/dt = 0 we have x = x0 and thus
u(x, t) = u(x0 , 0) = K (x0 ) = g (x0 ) = g (x)
u(x, t) = g (x)
b. For a ﬁxed x, we can integrate the PDE with respect to t
du
= − 3xt + K (x)
u
ln u − ln c(x) = − 3xt
u(x, t) = ce−3xt
Using the initial condition u(x, t) = f (x) e−3xt 247 ...
View
Full
Document
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

Click to edit the document details