A function f(x, z, y, t) of four variables, x, z, y, t, that satisfy the following PDE is called the heat equation:
Where a is a constant.
According to the heat equation, firs 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?
ft = α2(fxx + fyy + fzz),
(a) f(x,z,y) = e[29α1π2t +π(3x+2y+4z)]
(b) f(x,z,y) = 3x2 +3y2 – 6z2 + x +y – 9z – 3