(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the temperature distribution in an infinitely long cylinder of metal with insulated sides and initial distribution

u(x, 0) = 0, the absolute value of x < L

u_{0}, the absolute value of x > L

where u_{0}is a constant, is given for t >0, by

u(x, t) = (1/2)u_{0}[2 - erf((x +L)/(√4c^{2}t)) + erf((x - L)/(√4c^{2}t))

2. Relevant equations

u(x, t) = 1/√4∏c^{2}t∫e^{-(x - y)2}/4c^{2}t f(y) dy bounds = -∞<x<∞

3. The attempt at a solution

= (u_{0}/√4∏c^{2}t)∫e^{-(x - y)24c2t}dy

Then I know you make a change of variables but I am having trouble with finding my new bounds of integration after I make the change of variables?

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# Showing the temperature distribution in an infinitely long cylinder

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