What is the constant term, ( y₀ ), in the initial value problem solution ( y(t) = 9e⁻³ˣ - 6x + 5 ), given ( y'(x) = g(x) ) and ( y(0) = y₀ )?
A) ( y₀ = 5 ), ( g(x) = -3 )
B) ( y₀ = 9 ), ( g(x) = e⁻³ˣ - 6x )
C) ( y₀ = -6 ), ( g(x) = 9e⁻³ˣ )
D) ( y₀ = 5 ), ( g(x) = 9e⁻³ˣ - 6x )