Answer to Question #200100 in Differential Equations for Valasutean Emilia

Question

solve dx/(y-z)=dy/(z-x)=dz/(x-y)

Answer 1

$(1dx+mdy+ndz)/(1P+mQ+nR)=0$

$1,m,n, are \, multipliers$

$1dx+1dy+1dz=0$

$1(y-z)+1(z-x)+1(x-y)=0$

$x(y-z) +y(z-y) +z(x-y) =0$ $=\int (1dx+1dy+1dy)=0$

$x+y+z=C1$

$\int (xdx+ydy+zdz) =0$

$x^2+y^2+z^2=C2$