Question

please explain all, thanks

Solve the following integral equations for an unknown function f(x): (a) exp(-at?) f (x – t)dt = exp(-bx2) b> a > 0 f(t)dt (b) Sca 2 b> a > 0 (x-t)2 +a? 22 +62

Fourier Transforms, please explain in detail

Answer 1

fe-t)dt = -6 l>> [fox] = Facy.com) [a] - 吃 o) === Ja tiply on the both sides faues Tasostomy (FT) F{ a fe] = [] [fq-f[ 需 包RW - u D FW) = 一台) 元 Apply t 西 g on the both side Invest FT - > e 4 ) fina - 愛隱 ); 10) al ce) (四)~ a Rep = 。 MCG-5)

(6 off 466). I J2R dt= ,b>9>0 (2-4) 49² x2762 Soli fca* mitt ata² J2K 1762 F(40)] = f(w) Then f(f(») = a*fw) F[aarnya $F[ar] - Page 29 wzza Apply on the both sides Fourier Transforms fff} $ -alu) J2A 276 blw) → fra. I zawl 126. e a = F(W) = JA. -blwtaiw) a -Cb-a) Iwl q JZA. IMI(0-9) =J25. a b-a T To bra Apply on the both sides Invesse Laplace Tromdomos SF ( FCw]= von - (b-a) iw) b-a alb-o) Lumica.) БТ from alb-a) b 2² (6-9²