Solve d2y/dx2+6dy/dx+9y=12^-3x

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Shortcut for the Variation of Parameters.
How to solve a non-homogenous second order linear differential equation?
A method to skip "Let y=e^(mx)" for complementary function but it is fast and accurate.
Solve d2y/dx2+6dy/dx+9y=0 by inserting the dummy "m", fast and accurate. The complementary function for the associated homogenous equation, a faster way.
This method is applicable for all homogenous second order linear differential equations.
How to determine the particular integral for the non-homogeneous equation?
What is the general form of particular integral for the associated non-homogenous equation with exponential function?

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