I have a continuous dynamical system given by

dx/dt = x(y-z),

dy/dt = y(z-x)

dz/dt = z(x-y)

and have to show that for any initial condition

x0 , y0 , z0 such that

x0 +y0+z0= k for any constant k

the solution of the above equations will always lie in the plane

x+y+z=k

originally i tried to look at the solution, i got

(x(t),y(t),z(t) )= (e^(y-z)t , e^(z-x)t, e^(x-y)t)

but couldn't see anything to do from then onwards.

i think there's a nice and simple answer i'm just not seeing as it's only two percent of the sheet so i'm guessing sides of A4 covered in calculations are out.

cheers.