HW 4 UCLA - MAE 107 Homework objectives This homework has two objectives: 1. The first problem considers the first order ODE y = ay b1 u b2u. This ODE models several circuit topologies you have studied in prior homework. Note that this ODE can be considered as a "superposition" of two familiar ODEs: y = ay b2u and y = ay b1 u. 2. Problem 2 will help you consolidate your understanding of the convolution operation using a graphical approach. Turn in MATLAB code, as text at the end of your work. Problem 1 Consider the first order ODE y = ay b1 u b2u. Recall that two different circuits from previous homework problems are described by this ODE (of course, each circuit is associated with a certain set of {a, b1, b2} parameters). This problem continues the analysis of this differential equation. The impulse response has been derived in class and is: h(t) = eat(b2 ab1)(t) b1(t), where (t) is a step function defined as: (t) = 0 for t < 0, and (t) = 0 for t 0. We introduce the step function in our notation to make it clear that h(t) is zero for t