Question

Solve the given integral equation or integro-differential equation for y(t). y (t) + 125 [(-viy -vly(v) dv = 10t, y(O) = 0 0 y(t) =

Answer 1

Solutions given that + Yet + 125 Se- (t-v) gens d du lot > year gross t (+ of 125 Syers du as differentiating equation - 0 both sides and y" cos again differentiating q"et) + both sides, we get 125 yet) with yeas a gloo and gulosa aunillary equation + 125 = - 125 r? (x + 5) -Sv (+5) +25 (3 + 5) (72-58+05) (9+ 5) 0 r = 5 I 25-100 -5 6

5 & 5-75 - 5 8= 5 £ 53 i -5 then solution ý sly x yest ast се 11 e + -5t 512 com (3 034) + ç sin (EVG+) g'rt) = -5c, e (61 Cz.com ( 3 Vat) + sin (313) test li va co sie (8 964) . { vacan(5 vot! + inford yeol => cit C >> Carų gros : - - 56, +55 C2 + 5 13 = 0 Rol C₂ + 5 VIC=0 ₃ = (36₂ -5t + g" (t) = 250, e S(cz.com ( 3 Vot) + sin ({ v3+)) er et -csin ( vot) + G3 cos (634)) + esut (-28 , car (%6rst) - 23 Cg sin (252t)) + 253 e 2

y" com = 25C, + 25 cm + 25 13 ₂ 75 C2 But y"co) = 10 :. 356 +19) + 2513 250 50 4. C + 25 136₂ 17 -25C₂ 50 C 75 C2 10 4 C = -6 and e3=-v363) -25-5 - 19:10 100 - 50 - 150 C = lo - 300 C E 40 C2 TS C = 2 15 and 15

Yeste) 5.et -5t 2 e 15 of e cas 13t) +253 sin 15 sin (EVP) 15