Differential the two sides of the equation, e (x+2y+3z) d (x+2y+3z)+d (XYZ) = 0,

e^(x+2y+3z)(dx+2dy+3dz)+yzdx+zxdy+xydz=0，

Substitute x=y=z=0, dx+2dy+3dz=0, so dz=-(dx+2dy)/3.