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Prove. Given the function U(x, t) defined for a ole.gif x ole1.gif b, t > 0. Let the Laplace transform of U(x, t) be


             ole2.gif


Then the Laplace transform of ∂U2/∂t2 is given by



             ole3.gif


where


             ole4.gif



Proof. Let V = ∂U/∂t. Then


             ole5.gif


                                                = s{s L[U] - U(x, 0)} - Ut(x, 0)


                                                = s2u - sU(x, 0) - Ut(x, 0)


SolitaryRoad.com

Website owner:  James Miller


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