Question

The most suitable choice for the particular solution for the following equation is G. 30% + 2y = 5e2t sin(3t) dºy dt2

Answer 1

12 Solh given dy 3 dy Ita- dit +2y=seat 81713.) Put d de - D in e qh cis 7 D2Y-3 04+ 2Y 5 ezt 811 (34) - (02- 3D +2y = 5e2+ &in (36) P.I= as d (DJ Y = v v] f(D) .V Seat &in (34) D2-3D+2) ear = and &lhan Now We know P. I of deos ean f(0+2) riota einan f(02) frary Where f(D+9) 204 fl-a) to use the above Formula 12t sin (3+) (+2)2-3(0+2)+2 sin (3) D2+4+4D-3D-6+2 & in (34) 5 le >> s ezt = 5 e 2 + 02 + D

> 2 put D² (3) 2 > seat 8in (34) -(3) 240 5 e 0-9 ezt &ln (3t) =) 5 e 2t (D+9) D-9) (0+9) 81n3 +) 2 5 e2t (D+9) sin(3+) 02-81 5e2+ (0+9) sin (31) >) -9-81 s ezt 2t [ a la 81634) +9814B +) go ก ก s ezt [ 360x34) +9-816 (34)] -go - 5 e 2t [ Cal (36) + 381h (3+)] - 30 Hence suitable is Particular Solution of eahci, म [Cox(34) + 38in(34)] And -6