Question: Suppose f(x) is a smooth function, defined on the whole real line. Suppose c is a constant. Show that the equation au?(x, t) _ 2our

 Suppose f(x) is a smooth function, defined on the whole real

line. Suppose c is a constant. Show that the equation au?(x, t)

Suppose f(x) is a smooth function, defined on the whole real line. Suppose c is a constant. Show that the equation au?(x, t) _ 2our (x, t) at2 satisfying the requirement that u(x,t=0) = f(x) has solution u(x, t) = .5 * [f(x + ct) + f(x - ct)]

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