[SOLVED] Amath 569 homework assignment 3

1. (a) Solve using Fourier transform in x and Laplace transform in t:
PDE:
BC:
IC:(b) Same problem as in (a), except that you do not use Laplace transform in t.
You need to figure out the matching condition for your ODE across t=t.
2
2 uD u x t x t ( ) ( ), , 0, , 0
t x
d xd t x t ¶ ¶ – = – – – ¥ < < ¥ > -¥ < < ¥ >
¶ ¶
uxt x t ( , ) 0 as , 0 ® ® ±¥ >
ux x ( ,0) 0, . = – ¥ < < ¥