\fManage your time carefully! Problem 1 (2.5 marks): Simplify the following expressions a. [sin(t - 7/4)8(t - n/ 2) dt b. u(t) S(t + 1) Problem 2 (2.5 marks): Determine the order and clarify each equation as linear or nonlinear a. y' = -(2t + y)/2y b. y" sint =-t*+y+1 Problem 3 (12.5 marks): Given f(t) = e 'u(t -1) and g(t) = eu(t). Compute the convolution f(t) * g(t) using the graphical approach. Problem 4 (10 marks): Consider a continuous-time linear time-invariant (LTI) system. - When the input to this system is x(t) = 2e "u(t -1), the output is y(t), and - When the input is ax dt , the output is - 3y(t) +e "u(t) . Find the impulse response of this system. Problem 5 (12.5 marks): Solve the following initial value problem. dy -= ycotx + y>0 y(7/2) =1 dx sin x