286 ONL Exam 1 Practice(Solutions) - 1 Math 286 Practice...

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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[0] = 2.: Use the formula y[t] =-r tstarter +-r t0tr sf[s]s. y[t] = 2-3 t+-3 t0t3 s-2 ss0tss = t- 1, so y[t] = 2-3 t+-3 t(t- 1) = -3 t+-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[0] = 10, y'[0] = 0
d) Is this oscillator overdamped, critically damped or underdamped?: Since there are two different real roots, it is overdamped.1
3) You are looking at the diffeq(7 points)y[t] = y[t] - 2 t with y[0] = 1.When you go with Euler's method starting at {0, 1} and ajump size = 1, then the first three Euler points you get are {0, 1}, {1, a} and {2, b}.Give the precise values of a and b.: y

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