Question

Solve the integral equation: y'(t)1- y(t-)e2 dr. y(0) 1

Answer 1

Here the given integral equation is y' (t) = 1- Syet-e).se 27 dt with 101-1 Now t Sye-T)eude= y(t) *e r By convolution property) using @ in ☺ we get u - y(t) = 1- ytxe-2t Taking Laplace transformation on both side of o, we get L4 () - Ly - Lý - PLEY(+1} - Y(9) - L{ycy). the 17 - psy(t)}-1= -{y(t) Pt2 P+2 1fycv] [P+ Fi] = + => 1894**)= Papel : Sylt) LG 347 - P42 PH +1? - Goes Lsyst] = Pf2 Pop Fig.

PFI Pal = pel + Bari ... LfYx) = 3 - PA PA taking in verse Laplace transformation y(t) = L-157] -2-15 pt) = 2-et. y(t) = 2-et which is the required solution of the given integral tatuation