The wave equation c2 (2u/(x2 = (2u/(t2 and the heat equation c (2u/(x2 = (u/(t are two of the most important equations in physics (c is a constant). These are called partial differential equations. Show each of the following:
(a) u = cos x cos a and u = ex cosh ct satisfy the wave equation.
(b) u = e-ct sin x and u = t-1/2e-x2/(4ct) satisfy the heat equation.