Solve the given differential equation by variation of parameters. 3x2y" + 7xy' + y = x2 - x

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A: See explanation below for the answer.Explanation:

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A: Here, Let's consider 1st iteration :Hence the root lies between 2nd iteration :Here, The root lies…

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A: DETAILED SOLUTION IS PROVIDED BELOWExplanation:

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A: image uploadedExplanation:Step 1: Step 2: Step 3: Step 4:

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Q: Please solve and show all work.

A: The matrix [A​I​] is ⎣⎢⎡​12−2​01−4​3−3−3​∣∣∣​100​010​001​⎦⎥⎤​.  The inverse of the given matrix is…