Problems from Gabel and Roberts \"Signals and Systems\" 2/e or 3/e. where \"solv

Question

Problems from Gabel and Roberts "Signals and Systems" 2/e or 3/e. where "solve for y(t)..." is to be interpreted as "solve for the steady-state solution yp". where "what is the solution..." is to be interpreted as "what is the steady-state solution..." Solve the following equations using both the direct method and the convolution method. (D2 + 7D + 12 )y(t) = et xi(t), y(0) = dy(t)/dt = 0 For the system shown below, find a differential equation that relates y(t) and u(t). Solve for y(t) when u(t) = sin omega t xi(t) with a relaxed system at t = 0. Determine a system block diagram for which the input u(t) and the output y(t) satisfy the differential equation What is the solution to this equation when the input is u(t) = cos (omega 1 t) - sin (omega 2 t)?

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you are not allowed to ask so many questions in a single post pls split them in multiple posts thanks

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