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nintendofreak1
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$3.00 Laplace equation

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Laplace's equation: help with the question please
 
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Laplace.docx (239K)


   
   
   
   
 
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alephzero314
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$8.00 Complete solution with steps

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  • Posted on Mar 04, 2009 at 8:55:13PM
A:
Preview: ... = F''(e^t) e^(2t) + G'(t) e^(t) e^(-t)<br> = F''(e^t) e^(2t) + G'(t) <br>Thus:<br>F''(e^t) = (G''(t) - G'(t))/(e^(2t))<br><br>Let's sub that in:<br><br>e^(2t) (G''(t) - G(t))/e^(2t) + e^t (G'(t)e^(-t)) - n^2 G(t) = 0<br><br>giving:<br><br>G''(t) - n^2 G(t) = 0<br><br>G''(t) = n^2 G(t)<br><br>Let G(t) = e^(bt)<br>Then:<br>b^2*e^(bt) = n^ ...

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