One of the following is a general solution of the homogeneous differential equation [math]
[math] and one of the following is a solution to the nonhomogeneous equation [math] [math] By superposition, the general solution of the equation [math] is
[math]
Find the solution with
[math] [math]

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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