A function f (x, z, y, t) of four variables, x, z, y, t, that satisfy the

Question:

A function f (x, z, y, t) of four variables, x, z, y, t, that satisfy the following PDE is called the heat equation:
ft = a2 (fxx + fyy + fzz)
where a is a constant. According to the heat equation, first partial with respect to t is proportional to the sum of second partials with respect to the variables in the function. Do the following functions satisfy the heat equation?
(a) f (x, y, z) = e[29a2π2t+π(3x+2y+4z)]
(b) f (x, z, y) = 3x2 + 3y2 − 6z2 + x + y − 9z −3