試題詳解

17. Let L(.) denote the Laplace transform. Which of the followings are true?
(A) L(a₁ f₁ + a₂ ⋅ f₂) = a₁ ⋅ L(f₁) + a₂ ⋅ L(f₂), for all a₁, a₂ ∈ and for all functions f₁, f₂
(B) if L(f) = F(s), then = sF(s)
(C) if L(f) = F(s), then L( ⋅ f) = F(s)/(s+a)
(D) if L(f) = F(s), then L(t² ⋅ f) =  
(E) if L(f) = F(s) and L(g) = G(s), then L(f * g) = (F * G)(s), where * denotes convolution operation