When the Laplace transform is applied to the problem y" + 4y' + y=e", y(0)= 1. y'(0)= 2 the resulting transformed equation is Select the correct answer O (?+4s+1]Y=s+6+ 1 s+3 Ob (?+4s+1]Y= -s=6+ s+3 O(?+ 4s+1]Y=s+6+ s-3 Od (?+ 4s+1)Y = -s-6+ O (?+4s+1]Y=s-6+ 51

(3) Suppose the Fourier transform F(w)=re-wl, is known. Show that the inverse Fourier transform, viz., F='{F(w)}=f(t)=H 1+t?

5. Find the general solution to x₁ = 4x₁ + 2x₂ + 3et, x₂ = 2x₁ + x₂ + et using Laplace transform.