Part II. Writing the equation d² dt2 in the form of the system d dt X = U, X = x³ + x², x = x(t), dv = x³ + x² 4 dt x = x(t), v=v(t), == (1) (a) Find all the stationary points (x, v) (the points where d = 0, d = 0). dx dt (b) Find the corresponding linear system near each critical point. (c) (d) Find the corresponding linear system near each critical point. Draw a phase portrait of the system near each critical point. Draw a phase portrait taking into account the energy conservation, for each solution (x(t), v(t)) to system (2), (e) + W(x) = const where the potential energy is given by the antiderivative of -x³-x¹, x4 W(x) 4 x5 5 (2)

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