(a) Show that u(t, x) = e-k2t+ikx is a complex solution to the heat equation u/t =...
Question:
∂u/∂t = ∂2u/∂x2
for any real constant k.
(b) Write down another complex solution by using complex conjugation.
(c) Find two independent real solutions to the heat equation.
(d) Can k be complex? If so, what real solutions are produced?
(e) Which of your solutions decay to zero as t → ∞?
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a ut k 2 e k2 ti kx 2 ux 2 b e k2 t i kx c e k2t cos kx e k2t sin kx d Yes Wh...View the full answer
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