Question

\[\frac{\text dx}{\text dt}=\sigma(y-x)\]\[\frac{\text dy}{\text dt}=x(\rho-z)-y\]\[\frac{\text dz}{\text dt}=xy-\beta z\]
\[\sigma, \rho, \beta \in \mathbb R^+\]

Answer 1

the solution curves are unusual

Answer 2

what's that ... system of first order equation?

Answer 3

yeas

Answer 4

try solving this
dx dy dt
--------- = ---------- = ... = --------
sigma(y-x) ............. 1

Answer 5

do you know how solve this type of equation?

Answer 6

since you have three independent variables ... I don't think this is going to be easy.