So the first question
For the equilibrium points I assumed that they are at equilibrium when the equation is equal to 0
So dy/dt=(y-1)sin y
they are at 0 when y is equal 0,1,+-pi,+-2pi
but how do I know which one is a sink,source or node?
The same as for the second
the equilibrium for dy/dt = 3 y^3 – 12y^2 is when equation is equal to 0
so eq. points are 0 and 4 because dy/dt = 3 y^3 – 12y^2=(3y^2(y-4))
again how do I know which one is a sink, source or node
The second question I know that y(0)=1/2 is the only one that satisfy dy/dt = (y-1) sin y...why? Someone told me its because its between 0 less than y(t) less than kpi?
The same for the second one, I know y(0)=1 because its between 0 and 4, why? How can I derive the answer? I'm confused, especially when it comes to graphing