Question

Solve the given integral equation or integro-differential equation for y(t). t y'(t) + (t-vly(v) dv = 5t, y(O) = 0 fe-vy y(t) =

Answer 1

y(0)=0 both sides Ginen entegro differential equation y'lt) + Sisu (6-0) you) dve = 56 Apply Caplan transform tly'ces I (4-u) du] stolt let wly(t)} = 9 (3) ot + bo (noh W{y' (t)] = s9 (57-960) - S952 s gus) +b 1 gcu) f(t) du] = 5.5 whe al f(t)=t Alflev] = * yct) S fit)* ای S9 () +1 = s gcs) $2.965) (1176 *1974)9; 135128 s (S)94) (3+0) gcs) علي s gos? Itas $ ģis) - (Stu) (ss=0

S (S+1) Cs=s S C = ㅋ A CStc + (S+1) (5 st) stl s²sti 5 ACS st) + BS+) CS+1) put 5 - A Cl+I+I) quite the co-efficient of s² =) B=-A - - put s=o 5= A+C A: wis 철 o = At C-SA - 5 wiis 10 3 5 = + + 3CSH) SPS+1 S - (SHI CS-strl S-2 sLS+1 8늘를 늘 핸 르 C 한때 S [Sale Tic - - =한 - 중 De [cat Sn ce) = = etcs ge) -f Soft] 음 - - 비에 soo) ما EL = 세에