#Attendance Question 1: Is the SIR Model named after Sir Ronald Ross or something else?
#Answer: The letters in “SIR” represent what the model tracks: Susceptible, Infectious, and Recovered
#Attendance Question 2: Why is the principle of linearity not true for y’(t) = y(t)^2?
#Answer: y’(t) - y(t)^2 = 0
# y’(c*t) - y(c*t)^2 = 0
# c* y’(t) - c^2*y(t)^2 = 0
# A constant multiple of a solution y(t) does not yield a constant multiple of the differential equation. Therefore, a linear sum of solutions will not solve this nonlinear differential equation.
#Attendance Question 3:
# a1:= 5th digit of your RUID (1)
# a2 := 1st digit of your RUID (1)
# a3 := 2nd digit of your RUID (8)
# Solve by hand and Maple: a1*y’’(t) - a2*y’(t) +a3*y(t) = 0
#Answer by hand:
# r^2 - r + 8 = 0 
# (r-1/2)^2 -1/4 + 8 = 0
# (r-1/2)^2 = -31/4
# r-1/2 = +- sqrt(31)*i/2
# r = 1/2 +- sqrt(31)*i/2
# y(t) = e^(1/2*t)*(c1*cos(sqrt(31)/2*t)+c2*sin(sqrt(31)/2*t))
#Answer by Maple:
dsolve({D(D(y))(t) - D(y)(t) + 8*y(t) = 0}, y(t));
y(t) = e^(1/2*t)*(c1*cos(sqrt(31)/2*t)+c2*sin(sqrt(31)/2*t))
#Attendance Question 4: Why is the property that if a(n) is a solution so is c*a(n) not valid for the non-linear recurrence?
#Answer: Nonlinear recurrence equations cannot be reduced to a(n) = c*λ^n
# Therefore, sums of solutions to nonlinear difference equations are not also solutions.