Consider the function of two variables  u (x,t) = 2e-t sin (2x)  Select the option that gives a partial differential equation for which this function of two variables is a solution.  A. (∂2u/∂x2) = 4(∂2u/∂t2)  B. (∂2u/∂x2) = (1/4)(∂2u/∂t2)  C. (∂2u/∂x2) = - (1/4)(∂2u/∂t2)  D. (∂2u/∂x2) = -4 (∂u/∂t)  E. (∂2u/∂x2) = 4 (∂u/∂t)

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A: Both the parts are given below.