Solution 2.9.2.1 f(t)=e ;at 1(t);e ;a(t;T 1(t; T) Then F(s) = Lfe ;at [1(t); 1(t;T)]g = Lfe ;at 1(t)g;Lfe ;at 1(t; T)g = Lfe ;at 1(t)g;Lfe ;aT e ;a(t;T) 1(t; T)g = 1 s + a ; e ;aT e ;Ts s + a = 1;e ;aT e ;sT s + a Check: F(s) = Z T 0 e ;at e ;st dt = ;1 s + a h e ;(s+a)t i T 0 = ;1 s + a h e ;aT e ;Ts ;1 i = 1; e ;aT e ;sT s + a 1