I am confused about the definition of a linear equation.
First, why is the Lorenz system considered to contain three nonlinear equations? (https://en.wikipedia.org/wiki/Lorenz_system#Overview) They all look linear to me. I don't see any powers on any of the terms in any of the 3 equations (much less all of them).
Second, I just realized the obvious fact that any linear equation can become nonlinear by simply multiplying both sides by the variable (e.g., $y=x$ can become $xy=x^2$). So how can we make a distinction between linear and nonlinear equations?
(I am a high school Calculus student, by the way - we haven't gone anywhere remotely close to the Lorenz equations in class but I'm interested in them.)