Solve the heat equation

[math]

[math]

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using

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[math]


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[math]
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[math] u = dv = [math] u = dv =

[math] du = v = [math] du = v =

[math]   [math] [math]

[math]
 [math] [math] [math]

[math]
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[math]
 [math] [math] [math]

[math]
   [math]


[math]   [math]   [math] [math]

[math]
 [math]   [math]   [math] [math]

[math]
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Your overall score for this problem is