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Where a is a constant

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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

Reference no: EM131104991

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