Question

Find the general solution of the differential equations taking into account the initial conditions, using the parameter variation method:

y'"' + 4y' = t y(0) = y'(0) = 0 et y"(0) = 1

Answer 1

equm is, the given y" +49'r auxilary aunilary equn vis * mit 4m co g m (mp4)=0 o ma or ma I 2

the complementary femetion in Yea B Cos 27 e Simar vakkiation palameres, using yun) au (1) & ₂ (1) Cesar fuglt sinar. WC) Sinar 0 Cesar -2 Sin 28 -4 Cesar 2 W21 - 4 Singh -8 w, Cna lover er sinar 2 2002r 62 W, 11) a Einar 2 Casar 11 C 2 Cod 22 lo 16 Aula ། los 22 -2 Sinar =-2 Sinare

= (t) ہا نی 22 8 C, (0) + 2 Lot 27 ni Ug (Hay To (2 ranat + Co222) + eg ug (8)= r. (-2 Singa) » Ug(t) = 1/2 (sinar - 26 leser) + es syza + C2 Casar + C Sinar a 12 8 7 Tho (21 sinar los2r + Cost21 + Cost 22 - Sintara 2+ Linet Con 21 es y = a + Cg Con art es sin art 42 8 to let 16 (2r Einar Y()= 0 ) + Casun G + es ar 16 yl (o)= 0 » e3 co y" (O) = 0 a -402 + -|+11 3 ų a too

-2 the solurion idag د (۲) لا too allo los art 1 (24 Snart cosur corsun Am