Find the solution to the differential equation with the given initial condition y'' + 2y' - 3y = 9t + 8e⁻ᵗ , y(0) = -2 .
a) y(t) = e⁻³ᵗ- 2eᵗ + 4t + 9
b) y(t) = -e⁻³ᵗ - 2eᵗ - 4t + 9
c) y(t) = e⁻³ᵗ+ 2eᵗ - 4t + 9
d) y(t) = -e⁻³ᵗ + 2eᵗ + 4t + 9