Problem 1. (20 Points) Solve the initial value problem u_t = au_xx by using the Laplace transform. u_x(0,s) = sin(s), 0 < x < 8, -x < t < 0
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The Laplace transform of the PDE u_t = au_xx with respect to t gives: sU(x,s) - u(x,0) = aU_xx(x,s) The Laplace transform of the initial condition u_x(0,s) = sin(s) gives: U_x(0,s) = sin(s) Show more…
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