Question

Solve the given integral equation or integro-differential equation for y(t). y (1)+ Ja-vy(v) dv=5t, y(0) = 0 0 y(t)=D

Answer 1

410204 hiven qw+ !* (tv) yu dv : 17 both sich Apply Laplace transform tyl1t} + 14 d * 14 - 6) giu) dv} 7463 Sicht- 400) + 1 Y 4) = 7 7 (5 + 1/ / ] } est= S2 44 (30+ 1) 7 ý (S) = s3t 1 Apply inverse bolt sich trona form C. Place Thass} = tih 33+) I = (a-b) lah_abt6²) 442= 큐 (5+1) Cutsti) considy B S to se sal (5+1) (5²-5+1) C-SAT 4 - A C2 S + 1) + (BS+ () C+1) (5+1) Cast) (S) A (3-5+1) +(85+6) 6+1). put S =-1 in ein A (+1+1) + 0 1-34 - only werer 20

Company - temo O=A+B BE-=-113 B = -1/3 compainz constats termo I=A+C (=1-A c=1-1 3 c=213 from a "Q V3 -15 + 73 = + 33+1 3+1 s²sti 23 77 3 3 sti sti shaol as the - 1 + 1 +3 - -sta 3 3 st (5-1) + ta 3 Sti 11 wo (3-1) + (12) +4 (5+1) + $44+0) (su) +9 } 3 st 3 3

الا) 3 t 나 일 (5)+(2) 일회분 ㅗㅗ 부 -일) + 3 t 3 (S) +1 both sides laplace trong tom Apply inverse = 음행해로 일일 얼 발행 et sin J3 r eft cas or + E 3 V2 화 Tt I e 3 ezt Ginust a 5 fm . 차 (as 3 tt e Sinoz 나 (1h t 르누 3. S