For the Lorenz system with a = 10, p = 28, and fi = 8/3,
(a) verify that if (x(t), y(t), z(t)) is a solution with x(0) = y(0) = 0, then x(t) = y(t) = 0 for all t;
(b) find the solution with initial condition (0, 0, 1); and
(c) find the solution with initial condition (0, 0, z0), where z0 is any constant, and sketch its solution curve in xyz-phase space.
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