Question

Determine the intervals in which solutions are sure to exist. (t - 4)y(4) + e'y" + 6t4y = 0 Enter your answer in interval notation. Do not use inequality signs (e.g. <). Enter the intervals in ascending order. If necessary, enter og as 'infinity'. If there are fewer than three intervals, enter DNE in the remaining response areas. Valid on the interval(s): a) u a) u Click VAR would like to Chau Warfar thietetlen. Aan Chat

Answer 1

Sony Diven differential equacion is : CH-1)d" telj" +6774 = () Divide *(4-4) on both sides, we get (41) ACAU (A - 1 (649"+ 6.02 : $(4-4) j = 0 ft-4) (4-4) 7. + (-4) . » y al g" + Get y = 0 . We can write this as . . 79) + 0.3"' + i d'+ 0.4't =0 comprising this with gray + P y" + P p " + 839! + fyd=0 we get 1150, pa taj , Pg =0, Pup for P, and P3 . equals to zero. means are constant function and hence are continuous every where Now Poi = el hai cinave , has singular point at. A=0 and t=4 .so it is continuous for t to and f74.. Similarly Pu is continuou- for ft4 . Therefore, we get Pl and P3 are continuous in .(-os, o). Paper is continuous in (-109,0) 0 (0,4)004,80) and Pu is confinuous on (-10, 4) U (4,80) Taking Intersection of these three integral, coe gest. DSC-00,0) U10,41 01415): which is the required integral on which solution are sure to east so answers - infinity, o. , Infinity (ans)