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## Main Question or Discussion Point

I have this book that gives the following differential equation:

[tex]\frac{dx}{y+z}[/tex] = [tex]\frac{dy}{x+z}[/tex] = [tex]\frac{dz}{x+z}[/tex]

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

By the way, the book gives the answer as:

[tex]\sqrt{x+y+z}[/tex] = [tex]\frac{a}{z-y}[/tex] = [tex]\frac{b}{x-z}[/tex]

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.

[tex]\frac{dx}{y+z}[/tex] = [tex]\frac{dy}{x+z}[/tex] = [tex]\frac{dz}{x+z}[/tex]

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

By the way, the book gives the answer as:

[tex]\sqrt{x+y+z}[/tex] = [tex]\frac{a}{z-y}[/tex] = [tex]\frac{b}{x-z}[/tex]

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.