Consider the autonomous equation dx/dt = (1-x²)e^x. (a)

Last updated: 7/22/2022

Consider the autonomous equation dx/dt = (1-x²)e^x. (a) Sketch the phase line for the equation. Label each equilibrium as a sink (stable), source (unstable), or node (neither). b) Predict the asymptotic behavior as t→∝ of the solution satisfying x(0) = 0. c) Predict the asymptotic behavior as t→∝ of the solution satisfying x(0) = -5.