Question

Solve the given integral equation or integro-differential equation for y(t). y(t) + 125 | ce–vy(v) dv=8t, y(o)=0 y(t) =

Answer 1

t sely Given Integral eqh Y' (t) + 125 S €-u) you) dx = 8+ w 46 ) = 0 - (2) Convelation of t* y(t) Taking Laplace tramfarm bath side Lşy(+) (exy (U)} = ({st? L {y'(t} + 125 L{t} {{4 (t)} = 8 L{t} of eqn O + 125 IL

→ 2 (SYS) –46) +125() 40- 854 ( 18602 590-46 l{464)] = y(s), 1843 = SYS) +125 125 (1) YCS)] -46) 864 = (stie + 125(3)] YO - wring (2) ) o Y (S) T 8. S2 S + 125 52 125 ) 8 11 T X T y (5) (5 #125) y (5) (3) $2+(5) Apply Inverne Laplace transform L'{Y(s)} Lt 8 3 453

→ Y(t) = 8 tlsts you a falar qurs) - 56 () es -st e 75 sto St Sin (15134 13 J5 (61 (SP) 75 -st te 75 5.53 9 (1) 853 Sin 75 Cas 53t 2 ( -8.3 225 (Style + 8 -St e 75 4) Eqh (4) represent the general relation of eqh (1) with