Use the method of direct linearisation to determine the stability of

(a) the fixed point at x = pi for the differential equation dx/dt = sin x, and

(b) the only fixed point for the differential equation dx/dt = ln (x/a) , a > 0.

(Hint: ln(1 + z) ~ z for |z| < 1.)

In each case verify your answer using the method of linearisation by Taylor polynomial.