Question

PROBLEMS Problems 1 through 6 involve equations of the form dy/dt = f(y). In each problem sketch the graph of f(y) versus y, determine the critical (equilibrium) points, and classify each as asymptotically stable or unstable. Draw the phase line, and sketch several graphs of solutions in the ty-plane. 1. dy/dt = ay + by^2, a > 0, b > 0, y0 ? 0 2. dy/dt = ay + by^2, a > 0, b > 0, -? < y0 < ? 3. dy/dt = y(y - 1)(y - 2), y0 ? 0 4. dy/dt = e^y - 1, -? < y0 < ? 5. dy/dt = e^-y - 1, -? < y0 < ? 6. dy/dt = -2(arctan y)/(1 + y^2), -? < y0 < ?

          PROBLEMS
Problems 1 through 6 involve equations of the form dy/dt = f(y). In each problem sketch the
graph of f(y) versus y, determine the critical (equilibrium) points, and classify each as
asymptotically stable or unstable. Draw the phase line, and sketch several graphs of solutions
in the ty-plane.
1. dy/dt = ay + by^2, a > 0, b > 0, y0 ? 0
2. dy/dt = ay + by^2, a > 0, b > 0, -? < y0 < ?
3. dy/dt = y(y - 1)(y - 2), y0 ? 0
4. dy/dt = e^y - 1, -? < y0 < ?
5. dy/dt = e^-y - 1, -? < y0 < ?
6. dy/dt = -2(arctan y)/(1 + y^2), -? < y0 < ?

PROBLEMS
Problems 1 through 6 involve equations of the form dy/dt = f(y). In each problem sketch the
graph of f(y) versus y, determine the critical (equilibrium) points, and classify each as
asymptotically stable or unstable. Draw the phase line, and sketch several graphs of solutions
in the ty-plane.
1. dy/dt = ay + by^2, a > 0, b > 0, y0 ? 0
2. dy/dt = ay + by^2, a > 0, b > 0, -? < y0 < ?
3. dy/dt = y(y - 1)(y - 2), y0 ? 0
4. dy/dt = e^y - 1, -? < y0 < ?
5. dy/dt = e^-y - 1, -? < y0 < ?
6. dy/dt = -2(arctan y)/(1 + y^2), -? < y0 < ?

Added by Robert G.

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