Question

7: Problem 6 Previous Problem List Next (1 point) Determine the two singular points of the differential equation (x2-16)y (4 - x)y +(x2 + 8x+ 16)y = 0 List the points in increasing order: X Which of the following statements correctly describes the behaviour of the solutions of the differential equation near the singular point X1 A. At least one non-zero solution remains bounded near x1 and at least one solution is unbounded near X1 . B.All solutions remain bounded near X C. All non-zero solutions are unbounded near x. Which of the following statements correctly describes the behaviour of the solutions of the differential equation near the singular point x2: A. All non-zero solutions are unbounded near x2 B. All solutions remain bounded near X C. At least one non-zero solution remains bounded near x2 and at least one solution is unbounded near x2

Answer 1

Solution diffegential equation The given x-16)y4-)y'+ (x sx+6)y the the giuen diffegential aqualion with Compaure diffexential equation Secand oycky a Cya +a Cx)y0 Heae a2 C) xtyCx-4) Cxt4C-4 4,4 only when x=-4,9 clecolyax) ls equal to zex0 the points So singular points of tte gîven dliffesential equation. oe is megulan iS xegular and -4

(b): The diffexenal Solulons af the behouio of the singulars point X eauation bounded neos Solutions emoun All opion B is coraect . difenental solutions of the The behauiou the of neau ingular point equation bouncled neo& emain Solutions Atl 2 OPtion -(B) Is co3dect.