In this exercise you will solve the initial value problem y'' - 16y' + 64y = e(-8x)/(1+x²), y(0) = 5, y'(0) = 2. Let C₁ and C₂ be arbitrary constants. The general solution to th...
a) y(t) = e⁸ᵗ) + e⁸ᵗ
b) y(t) = e⁸ᵗ * (C₁ cos(8t) + C₂ sin(8t))
c) y(t) = e⁸ᵗ * (C₁ sin(8t) + C₂ cos(8t))
d) y(t) = e⁻⁸ᵗ * (C₁ sin(8t) + C₂ cos(8t))