Originally Posted by

**hansbahia** Yea you are right, there is only y

sketch the phase lines for the given differential equation. Identify the equilibrium points as sinks, sources, or nodes.

(i) dy/dt = (y-1) sin y (ii) dy/dt = 3 y^3 – 12y^2

b) In this problem, a differential equation and various initial conditions are specified. Sketch the graphs of the solution satisfying these initial conditions. For each problem, put all your graphs on one pair of axes.

(i) Equation from a) part (i): y(0) = 1, y(-2) = -1, y(0) = ½, y(0) = 2

(ii) Equation from a) part (ii): y(0) = 1, y(1) = 0, y(0) = -7, y(0) = 5

These are the questions

But I can't understand how to indentify what they are asking. My book only says if y=y1 is called sink because the neighboring solutions are attracted to it as t goes to infinity. Equilibria that repel neighboring solutions, like y=u2, are known as sources; all other equilibria are called nodes, y=y3. Sources and nodes are unstable equilibria. That doesn't help at all. I tried to look online for phase lines, but there is nothing, not even examples