Q1-P2

[Victor Ivrii]

Find the general solutions to the following equation:
\begin{equation}
u_{xyz}=\sin (x)+\sin (y)+\sin(z)
\label{eq-1}
\end{equation}

[Roro Sihui Yap]

$ u_{xyz} = \sin x + \sin y + \sin z $
$ u_{yz} = - \cos x + x \sin y + x \sin z + f_{yz}(y,z) $
$ u_{z} = - y \cos x - x \cos y + xy \sin z + f_z(y,z) + g_z(x,z) $
$ u = - yz \cos x - xz \cos y - xy \cos z + f(y,z) + g(x,z) + h(x,y)$