Question

2. In each of the following problem sketch the graph of f(y) versus y, determine the equilibrium solutions, and classify each one as asymptotically stable, asymptotically unstable, or semi-stable. Draw the phase line, and sketch several graphs of solutions in the ty-plane. Here y0 = y(0).

(a) dy/dt = e ^y − 1, −∞ < y0 < ∞

(b) dy/dt = (e^-y) − 1, −∞ < y0 < ∞

(c) dy/dt = (y^2)* (1 − y)^ 2 , −∞ < y0 < ∞

(d) dy/dt = y(1 − y ^2 ), −∞ < y0 < ∞

Answer 1