Consider the Cauchy problem for the linear one-dimensional wave equation

where ƒ € C²(R) and g € C¹(R). Show that if f is an odd function and g isan even function, then for every fixed t > 0, we have u₂(0, t) = f'(3t). ) Without proving, write down the Laplace equation in polar coordinates.Using the method of separation of variables, find a function u(r, 9) harmonicin the annulus (2