Question

please answer alll! its greatly appreicated

Find a general solution. u" + 33u = 0 u(t) = [.

Answer 1

.) ull tul-20-los C-32) All we can write Mitula cosan +11+20 as cos (-30) -Cosin y" tul a cosin +31 (Note that 2015 A) we need to find partralan not multiplied with solution using Annin rafor method, before ul that we need to solve complemen baj gopago the differential equation -DCoti) = 0 21 m Conti) mao or morl D² to 20 20 a solution be y 9 tegen Now Assume the solution of the type Up = Cocos 3x & Cysmaa Now DYP 2 -3(3 em 30 at 3c4 cos Bal s² up a aqCz osan - 9 lysm 3x Now put mua

-9 G los an r9cy Em un -3 lasman +3lycosan we can write cos 3nt 31 Cossu (-969 +364) + SM. 31 (-9C4 -3() -Cossn +3 21 -9637344 =1 & comparing both -aly-3(3=31 soles we get Meeltoply, 39 and equation -963+3C421 - 9 C3 - 2764 93 + + 3064 -92 al Cya -92 46 30 15 Now put in one of the above egn -963+31-46). 21 : -903 = 14 46 es 2 2 X 17 5 to 15 2) Yp 2 - 1 / 2 cosan tsh Cosan +1 sman is soin

GOYA 68161 66&lae ସ୍ଥାବାd rnion 69 6619 କଟା(୧ ) 21101 216691. Agam at ask to find the operator that annholate Let uz cas 31 4 11 D(Coson til) -35min D²(cosantll) -900137 Düt que ad cos sn + q ecossat 1)) 9 losan tacossa of 99 m) D? +9 14 399 annhalate the equation D(D²tqj u 20 a 99 + 8y +12y = 840-sma it as to find the from of partreular solution not the particular solution che need to frad homogenous som m²+8 m+ 12 20 .8t 182_4x12 -82 Joy-48 ma so 2 2 &ty -12.00 14 y = e en thee? - 6 or -2 Now right hand side contams, expected contact u.c for Qua { x 403 Uoc for soma į smo, cosa} form of particular colution be Up a Geur tema + Groom

ay Now we need to find the operator (soy e 49-some au that annihilate Du= 4 eya 4 en a-cosa 0²y = 16040 of sma

2 D СА очечни (от (вечи в п Du toy a вч 41 +1 ЧА 0 ( 20 ) 4 1 4 2 ЧА - А (outpu ) - ) 1.9 -*- Ар? - 4р) и го каз)