Find the general integral of the pde $(y+x+u)u_{x}+(z+x+u)u_{y}$ $+(x+y+u)u_{z}=x+y+z$

 The auxiliary equations are

$\frac{dx}{y+z+u}=\frac{dy}{z+x+u}=\frac{dz}{x+y+u}=\frac{du}{x+y+z}$