Word Count : 275

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The given equation is: \[ (D^2 - 2DD' + D'^2)z = 12xy \] where: - \( D = \frac{\partial}{\partial x} \) - \( D' = \frac{\partial}{\partial y} \) ### Step 1: Solve the Auxiliary Equation The corresponding homogeneous equation is: \[ (D^2 - 2DD' + ___ _____ _____ ________ ________ _______ ________ _____ _______ ______.
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