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Initial Cond: u(x,0) = e

^{-x}

Now they say plug this into the general formula:

u(x,t) = 1/(4[itex]\pi[/itex]kt)

^{1/2}∫ e

^{-(x-y)1/2/4kt}e

^{-y}dy where k is a constant

now the first step they say is completing the square of:

-( x

^{2}-2xy+y

^{2})+4kty/4kt

with respect to the y variable, and they get:

- [(y+2kt-x)

^{2}]/4kt + kt - x

Now I could not get this, I also tried expanding out the final result and reverse engineer the result but in doing so I got stuck with an extra term:

y

^{2}+ 2y(2kt-x) + x

^{2}+ (2kt-x)

^{2}- (2kt-x)

^{2}

this step is when I perform the process of completing the square before trying to factorize everything and it is here that I am having trouble. Please help if you can I have the midterm in a couple hrs.

Thanks