One of the following is a general solution of the homogeneous differential equation $y''-7y'+12y=0$
and one of the following is a solution to the nonhomogeneous equation $y''-7y'+12y=6e^{x}$ By superposition, the general solution of the equation $y''-7y'+12y=6e^{x}$ is
$y =$
Find the solution with
$y =$

Being the highly trained differential equations fighting machine that I am, I checked the Wronskian (using the solutions to the homogeneous equation without the coefficients a and b) for good measure, and found it to be . The fundamental theorem tells me that that this is the unique solution to the IVP on the interval .

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