In this problem you will use variation of parameters to solve the nonhomogeneous equation y′−6y+9y = 2e³ᵗ
A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.)
_____
B. Write the fundamental solutions for the associated homogeneous equation and their Wronskian.
y₁ = __ y₂ = ___
W(y₁,y₂) = ___
C. Compute the following integrals.
∫(y₁g/W)dt=
∫(y₂g/W)dt=
D. Write the general solution. (Use c₁ and c₂ for c₁ and c₂).
y =____
(Note: Your general solution will only be correct if it is a general solution to the differential equation.)