Question
find the general solution for 14,15,16
differential equation
14. zt) 1 -5 21) =(0) 15. z(t) = 10 0 2 1 -2 (t) 3 2 -1 16. x(t) = -3 0 2 1 -1 0 (t) -2 -1 0
Recall: Given two functions f(t) and g(t), which are differentiable on an interval I, • If the Wronskian W(8,9)(to) #0 for so
0 0
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Answer #1

Que 14. solution. Given , (t) n(t) -5 ie racist) A milt) 012 (1) con M (t) 2 - where , AE اسے - - Now, A-AI! 20 -) 2 1-1 -5then , 교 U2 (312) , Take U,=2 then we get 1 i 2 15 11 (3-] Then 2 31-1 Now let Jy is since , U2 31-1 is an eigen vector of tyThen the is 2 Bin (37) -]+s{scombe)-timet general solution of equation r(t) = a qi(t) +2 ult) 2Con (3) = 4 -Cop(8t) - Sin 8 tIf eigen vector corresponding to do is up then [A-A, 1] To Bi 0 2 1-13 i -2 3 2 -1-13 18:00 1.3 :) (1-53 i) vi 2U, +(1-13 ) Uni (t) = elita ا to it 0 e 13 2 [Conc.TB +) i Ain (13 )] + 3 2.0 2 tenlis y este) til 15 15 ) = fantes, a fuerung -COA(13 t) -13 Sin(J3 ++ips3 cop(8t) + Bindst)} 2 Cos (13 t) + i sin (13 t81 (t) = 166 +13 (2) COA (134) +(62 - 134) fin (13 t) 2G Coulis t) + CZ sin (18+) If the eigen vector corresponding to alig ing(t) = gel 2 Then Filt) = R (E t the general solution of equation ① is, ñ (t) + molt 2 e |(6,+ 13 (2) Con (18+)+(52 -1361) Bn To +(3+44+02) +2 +4 +48 = 0 13 +4 +2 +74+ 6 =0 13 +212 +212 +44 +34 +6 =0 72 (x+2) +20 (4+2) +3(4+2) =0 (+2) (112 +21+3) =0s then, si 11 559 ht |(24) a take u,=2 then, 2 ū. -idz (2 + 12 v) If the solution we get from the first eigen value and eigen2000612+)-12 finkat)] 12 con(18+) +2 Sin (12 t) 2 cop (2 t) 122 sin (2 t) -t e 2 sin (2 t) -12 contrat) = ùilt) ti ū (t) (o atake n = 6 we get, 6 15 2 from the third eigen value then the solution we and eigen vector is, enzt. og Hy(t) с. е. 2t с. е 3

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find the general solution for 14,15,16 differential equation 14. z't) 1 -5 21) =(0) 15. z'(t)...
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