QI. A real LTIC system with input x(t) and output y(t) is described by the following differential equation: (D³ + 9D)y(t) = (2D3 + 1)x(t) %3D Assuming y(0) = 4, ÿ(0) = –18, and ÿ(0) = 0, determine the system's zero-input response %3D %3D

The input x(t) and the output y(t) of a nonlinear system are related through the following differential equation y(t) = x2dx/dt + 2x Prove that the describing function of this system can be given by √A6ω2/16+ 4A2 ejtan−1(A2ω/8)

After 25 years, your savings account has now grown to $16,200 and has an interest of 6.1% that compounds continuously. How much did you deposit at the beginning of the account

Consider the (linear inhomogeneous) ordinary differential equation df +2f(x) = x². dx (i.) Find a particular solution of this equation by guessing a solution of the form fo(x) = co + €₁.x + €₂x². (ii.) Find the general solution of this equation by solving the associated (linear homogeneous) ordinary differential equation +2f(x) = 0. (iii.) Establish that the solutions are closed under affine combinations (i.e. the solutions form an affine subset of functions).