Consider the autonomous equationdx/dt = (1-x)e^x.(a) Sketch the phase line for the equation. Label each...
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Calculus
Consider the autonomous equationdx/dt = (1-x)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.
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