Math 286Practice Exam 1Show all work on this exam. Support your answers for full credit. No credit will be given for unjustified answers.Noscientific calculators, computers, or Mathematicamay be used -- 90 minutes allowed for this exam.1) Come up with a formula for the solution of the following diffeq: (6 points)y′[t] + 3 y[t] = E-2 twith y = 2.: Use the formula y[t] =ⅇ-r tstarter +ⅇ-r t∫0tⅇr sf[s]ⅆs. y[t] = 2ⅇ-3 t+ⅇ-3 t∫0tⅇ3 sⅇ-2 sⅆs∫0tⅇsⅆs = ⅇt- 1, so y[t] = 2ⅇ-3 t+ⅇ-3 t(ⅇt- 1) = ⅇ-3 t+ⅇ-2 t2) (16 points)a) Write down the characteristic equation for this unforced linear oscillator .
b) Solve the characteristic equation.: (
c) Find the solution for the oscillator given the following initial (starter) values:y = 10, y' = 0
d) Is this oscillator overdamped, critically damped or underdamped?: Since there are two different real roots, it is overdamped.1