Although there are exceptions, per class, many of the differential equations that you will have to solve as an electrical and computer engineer, in particular those that have to do with circuit analysis, are linear ordinary differential equations with constant coefficients. we will consider first-order versions of such this week and second-order versions of such next week. this means that the differential equation in this problem will have the form yay r(t) where r(t) is the input (sometimes called the "forcing function") (a) find the homogenous solution y(t) of this differential equation; that is, find the solution when r(t) 0. (yes, i know this is easy.) (b) find an expression for the entire solution y(t) +cyn(t) of this differential equation as a function of a and r(t). (note: you will have an integral in your answer that you will need to leave, since you do not know r( (c) use the knowledge you have gained for this special case (constant coefficient) of first-order linear ordinary differential equations to find the entire solution to the following initial value problem y'2y 4t y(0) = 2