Simultaneous differential equation

[ForMyThunder]

I have this book that gives the following differential equation:

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

Could anyone give any suggestions on how to solve this? Thanks.

By the way, the book gives the answer as:

\sqrt{x+y+z} = \frac{a}{z-y} = \frac{b}{x-z}

I think that there should be some kind of substitution, but all I could think of was u=x+y, u=x+z, u=y+z, and u=x+y+z. All of them came up short.

 

[ForMyThunder]

Wait, the actual differential equation is:

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