Consider the Cauchy problem for the linear one-dimensional wave equation 9 Uzz for x €R and t > 0, = "n u(r,0) = f(x) for r E R, u(r, 0) = g(x) for r E R, where f e C²(R) and g E C'(R). Show that if ƒ is an odd function and g is an even function, then for every fixed t > 0, we have uz(0,t) = f'(3t).

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