Question

a) dx/dt = x(1-x^2) b) dx/dt = x(x+2)(x^3-1) draw a sketch of the function dx/dt as a function x, draw the phase line,classify them as stable or unstable with equilibrium points,predict the outcome of the solution if the system starts at x(0) =0.5.

Answer 1

\[\Large \frac{dx}{dt}=x(1-x^2) \] let m denote the slope dx/dt, such that:
\[\Large -x^3+x=m \] For the sketch I would choose easy values of m such that you can solve the equation above, this will help you explore the integral curve a bit, doesn't seem too easy though for this one.

Answer 2

in my text book .. its says find equilibrium points first and depends on equ points we draw sketch... but here -x3 =0 ,x=0 means only one equilibrium point... so how i draw the sketch..