1) Differential Equation: y” – 14y’ + 85y = 0 by Aaron Libato
a) characteristic polynomial:
Take coefficients for each degree of y then sub into polynomial.
Ar^2 + Br + C = r^2 – 14r + 85
b) list roots from characteristic polynomial:
roots in this case are obtained from the quadratic formula of
(-b * sqrt(b^2 – 2ac))/(2a) = (14*sqrt(-14^2 – 2*1*85) / 2*1
r = 7+6i or 7-6i where lambda = 7 and omega = 6
c) list the basic solutions:
y1(t) =( e^7t )*sin(6t)
y2(t) =( e^7t )*cos(6t)