show that both
x₁ (t) = e⁻ᵗ cos t and x₂ (t) = e⁻ᵗ sin t
are solutions to the second-order differential equation
x" + 2x' + 2x = 0
Show that
x (t) = Ae⁻ᵗ sin t + Be⁻ᵗ cos t
is a solution for any values of the constants A and B.