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:

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