28   9. A particle P moves along a straight line. At time t minutes, the displacement, x metres, of P from a fixed point O on the line is modelled by the differential equation t 2 d d 2 2 x t – 2t d d x t + 2x + 16t 2 x = 4t 3 sin 2t        (I) (a) Show that the transformation x = ty transforms equation (I) into the equation d d 2 2 y t + 16y = 4 sin 2t (5) (b) Hence find a general solution for the displacement of P from O at time t minutes. 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over 29   Question 9 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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