# Three Variable Simultaneous Differential Equation

1. Jun 1, 2008

### ForMyThunder

I have had a troubling time trying to solve this equation out of this book I have (not homework, just for fun). Here it is:

dx/(y+z)=dy/(x+z)=dz/(x+y)

I've tried the substitution u=x+y+z, du=dx+dy+dz but I couldn't arrive at an answer. Any suggestions?

2. Jun 1, 2008

### ForMyThunder

If it is any help, the answer is given as:

sqrt(x+y+z) = a/(z-y) = b/(x-z)

I think I've solved this equation before but I can't remember how.