After an ice cube is placed in a 10cm glass of lemonade, it sinks to the bottom of the glass in seconds before the ice bobs up and down. A hypothesis is that the sum of the acceleration of the ice, the velocity of the ice cube, and the vertical position of the ice in the glass is proportional to e^(t)+ sin(2t). a. Find a differential equation modeling the vertical position of the ice in the glass. b. Find an initial value problem modeling the position of the ice in the glass. Be sure to explain your choice of initial conditions using words as well as equations. c. Solve the initial value problem.