Example. show that the differential equation satisfied by the family of curves gve oy 2 1 = o, where c is the parameter of the family, is mathematics (different

Example. Show that the differential equation satisfied by the family of curves gve oy 2 1 = O, where c is the parameter of the family, is Mathematics (Differential Equations- satisfied by the family of curves given by c + 20 2cy (1 x2) p2 + 2xyp + x2= 0, where p = dy dx Sol. From the given equation of the family of curves, we have, on differentiation witn re 2cp 2x = 0. Therefore C = p Eliminating c from the given equation, we get the corresponding differential equation as 2xy +1-0 P or, (1 x) p? 2xyp + x = 0. Ohtnin tha differential equation of the svstem of confocal conics