Part II. Writing the equation d² dt2 in the form of the system dx d dt (c) (d) (e) = V, = x³ + x², X = V= x³ + x² W(x): x = x (t), = x = x(t), v = v(t), (a) Find all the stationary points (x, v) (the points where d = 0, dt (b) Find the corresponding linear system near each critical point. 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, 12/201² v² + W(x) = const for each solution (x(t), v(t)) to system (2), where the potential energy is given by the antiderivative of −x³ – x4, x4 10/2/20 dv dt x5 (1) (2) = 0).

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