Question

10. Use any method to solve the problem: 4y" – y = eX/2 + 4,

Answer 1

Solution - Griven 48"_yze 48"_y2 % 244 * 4 dzy y 242 +4 dÝ ? this as Cinear differential equations with constone coefficient Thus, the general si al solution of equn ③ Cofot Pozo ♡ 95 ga Where Cofoc complementary function I involves an ari bitony constant and ol Poşticulor Integral) does not in volumes any anibitory Constont Perol

given C ce Mit fcq e Max. Now, the eo en can behawollen al (41)1..1) g. whene the auxi lan y requt of 6 ve and fineling coln 402-10 빛 Md = 1/2 mar 10 (say) roots of auxilary of equn 6 is distinct pont of cofo is of the type C.e 1 40% = 1 D2 = 1 4 DE I 2 0 Corresponding is Hence equn 6 to fors of the form. Coro 1/2 cle 469 cm / Porticular finding (P.10) - integral 1. 402.1 Cell +4) Poto - using 4 : 400x 1 4 Det (29240°9) 1 4.00x eX/2 t poi 4.02. 40²1

cusing these property Ps . 1 e ax - 1. fal ean fialto fo) 1 xh e9x р: 1. 2. 3.. fiDzajn ก! So 1 — е. 4 ебу + 1 4p2, 1 par: 4 02.1 (0) 11 , let Isa 1 ч. 4 ?- 2 if Da property @ ºs Not valid (3) poptsty using the we get so 1 1, а е?, 402 - 1 1 ex, [ using using &2=6% (046)(26 (20-1) ( 2 )+1) pm pelta (2) again using

1 x42 7= 20-1) 2X4+1) مرد دارد که Ij 1 e 42 2 12D-1) Now using property B I 11- L276fbeen? 1 lo (20- letz 412 = r II e LL z 4 4 0X12 4 eor I 2 = 1 402_1 eox 2 4. 40²-1 (2 using property 4 ea one Jaz 2 4x0 -1 4 ot [.-20%, 1 To r Los 4 From 12 & La value susstuted in A SO IN P. 1. x el 2 - 4 4 sus stated the value of equn of equiem in equn 0 and we get solution of equh

xht 12.4 yo Ciem of C2 e a el 4 this is required solution Thanke