∂u∂x+∂v∂y+∂w∂z=0.\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0.∂x∂u+∂y∂v+∂z∂w=0.
1)
8x+4xz+∂w∂z=0,8x+4xz+\frac{\partial w}{\partial z}=0,8x+4xz+∂z∂w=0,
w=−∫(8x+4xz)dx=−8xz−2xz2+C.w=-\int(8x+4xz)dx=-8xz-2xz^2+C.w=−∫(8x+4xz)dx=−8xz−2xz2+C.
2)
8x+3y+∂v∂y+3z2−2y=0,8x+3y+\frac{\partial v}{\partial y}+3z^2-2y=0,8x+3y+∂y∂v+3z2−2y=0,
v=−∫(8x+y+3z2)dy=−8xy−0.5y2−3yz2+C.v=-\int(8x+y+3z^2)dy=-8xy-0.5y^2-3yz^2+C.v=−∫(8x+y+3z2)dy=−8xy−0.5y2−3yz2+C.
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