A 2nd order Taylor approximation is just a parabola with well-chosen parameters. It's only the X that is changing, but \(x_0\) is the steady state, original endowment, etc. Will need to be able to crank out simple ones-- good for local analysis but dangerous in aggregate systems.
Bernoulli Equation
If \(\dot y + ay = by^k\) then one can substitute \(v = y^{1 - k}\) in order to solve for the first order differential equation and then substitute back: \(y = \frac{1}{v(1 - k)} \) and \(\dot y = (\frac{1}{1 - k}) \frac{k}{v(1 - k)}\).