Solve for X(x,y,z), Y(x,y,z), Z(x,y,z) { (((∂Z/∂y)−(∂Y/∂z)=1−x^2 )),(((∂Z/∂x)−(∂X/∂z)=−(y^2 /2))),(((∂Y/∂x)−(∂X/∂y)=z(2x−y))) :} where { ((X(x,y,0)=0)),((Y(x,y,0)=0)),((Z(x,y,0)=0)) :}


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Question Number 110262 by Ar Brandon last updated on 28/Aug/20
$Solve for X(x,y,z), Y(x,y,z), Z(x,y,z) { (((∂Z/∂y)−(∂Y/∂z)=1−x^2 )),(((∂Z/∂x)−(∂X/∂z)=−(y^2 /2))),(((∂Y/∂x)−(∂X/∂y)=z(2x−y))) :} where { ((X(x,y,0)=0)),((Y(x,y,0)=0)),((Z(x,y,0)=0)) :}$
$Solve for X (x, y, z), Y (x, y, z), Z (x, y, z)$ ${\begin{cases} \frac{\partial Z}{\partial y} - \frac{\partial Y}{\partial z} = 1 - x^{2} \\ \frac{\partial Z}{\partial x} - \frac{\partial X}{\partial z} = - \frac{y^{2}}{2} \\ \frac{\partial Y}{\partial x} - \frac{\partial X}{\partial y} = z (2 x - y) \end{cases} where {\begin{cases} X (x, y, 0) = 0 \\ Y (x, y, 0) = 0 \\ Z (x, y, 0) = 0 \end{cases}$
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