Hi people! This is my first topic here so excuse me if im doing smth wrong) So basically im having problems with understanding of how to sketch the graphs of solutions of diff. eqs in terms of y and t... Here is the description and 2 problems: Problems 8 through 13 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 one as asymptotically stable, unstable, or semistable (see Problem 7). dy/dt = y(1 − y2), −∞ < y0 < ∞ (1) dy/dt = y2(1 − y)2, −∞ < y0 < ∞ (2) so for (1) i have the following: f(y)=-y3+y and the roots are f(y)=0 then y=0,1,-1. so for each interval we have: −∞,-1 (+) -1,0 (-) 0,1 (+) 1,∞ (-) which means that -1 and 1 are stable crit. points and 0 is unstable I have a cubic parabola for f(y),y plane and i dont know how to interpret all this data in terms of y,t plane for (2) 0 and 1 are both semi stable points since the function doesn't change its sign.. same story,cant move to t,y=( Please help me to understand the idea here! would be great to see ur sketches=) Thank u all!