I attempted this differential equation but couldn't find the answer to part (c) of the question!
This question is about the differential equation dy/dt = y^2 - 4y + 2.
(a) Find all equilibrium points. Determine whether each equilibrium is a sink, a source, or a node.
(b) Sketch the phase line
(c) Describe the long term behaviour of the solution to the differential equation that satisfies the initial condition:
(i) y(0) = 0;
(ii) y(0) = 1;
For part (a) I found the equilibrium solutions as y=2+sqrt(2) and y = 2-sqrt(2) with y=2+sqrt(2) being a source and y=2-sqrt(2) being a sink. For part (b) I made the phase line having both the equilibrium solutions and the directional arrows. I however couldn't find the answer to part (c) of the question. I couldn't find anything similiar to part (c) either. Help please. Thanks!