A mechanical oscillator (such as a mass on a spring or a pendulum) subject to frictional forces satisfies the equation (called a differential equation)

y"(t) + 2y'(t) + 5y(t) = 0,

where y is the displacement of the oscillator from its equilibrium position. Verify by substitution that the function y(t) = e^-t (sin 2t - 2 cos 2t) satisfies this equation.