Question

Solve the given integral equation or integro-differential equation for y(t). y'(t) +27f (t-vjy(v) dv=7t, y(0) = 0 y'a ajia-rom y(t) =

Answer 1

wir.t. t we Ginen t with y=- y(t) = 77 = 7+ – 27 f(+-v7 7603 dv 2 (tar) yuz . dr "(+/= 7 - 27 (t-17.4641-04 Y CE1 = 7 - 27 r s gen) dr I Szendr & from Dilin y"(0/=.7 yol gebe O as trial solu temt SIN 42/25=-11- SIN itle ttg sint Again Difen ② were to I wore to t we Y(+2= 277 (+) ? + 27 84+1=0 Then pul yt) quaillar canalion becomes mit 27 =O man3,030,-3w2 ost 9(+) = C, et leccosistent nument Now with fnitial condition ycol=0 0 = 9, + cz [G=-62 I'(t=-3 e, est + feasintat i la costele -Ź ( Cz costat ht) e42 - 3e, trees - Ź CZ seit ² C sin' = with 4'601=. 0 11 ya 43 C3 ass- 39 - ²9,- Se Scanned with CamScanner. 59 = 3₂

3반 웨이, 웨 A. 아 2 Cost 볼t (t = - 2 e e2 [Les ( C - 몰 볼 Sn틀 -글 C05플 "(t) = 9 crea [cs ( Nit - cs | + 22 (-24 sintet (이t ㅋ + Lcs(o - ) 7. . 4무23 g풍23 =g7 Again, 에서 다 sciss S 39 A CF - 옳이 ㅜ 197 젖며 23 34 쭭 급 피브 +0 bl 23름() (t) - + The reamed sin 8 부에는 분 C0s를다 4631 703 sintet sinft 자 T QS 시는 가 51 ) CS Scanned with CamScanner A