Question

I need help with this question of Differential Equation.

Thanks

Solve the given integro-differential equation by using the Laplace transform: (t) + 4' (t) = ['since sin(t – T) (t)dt, 4(0) = 2

Answer 1

Given t 010)=2 Q17) † o'ct) Sin (+-4) & (T) dy Taking laplace transform tolh side, we get L(Plt)) + 110!+)) 21+)) L (sint) =) -($16) + 5 4(Plt))– PLO) = 2(P1+)) 2 (014)) (?+s - Ste] (.:060)=2) 3+1 - 2 =) + 2 s 2 (its) =(1-(14) (1+s)] (1770) 7 (1 +5) = (s +18+ęs) (1+2017 ((+20)2 Cites) (i+s+s)s [s -(1+5+5) = (itstus)s + i+stus -]

= 2 ... L(01) (S++)7 Taking inverse Laplace toomsform, ['s styti we get 2 9 Lt) = a[5'(+) - a gy sin! =)] [ - 21 é žt