Assignment:
The differential equation
y" = -ky - cy'
is used to model a motion of a mass on a spring with damping, where k is the spring constant and c is the damping coefficient.
a) Show the function y = e^-t cos 3t satisfies the differential equation y" = -10y - 2y'.
b) Show the graph of y(t)
Provide complete and step by step solution for the question and show calculations and use formulas.