Determine a 3 × 3 matrix A that could appear when the third order differential equatic 3y" – y" +y' = 0 is converted into a system of first order differential equations as x' - = Ax where x is a 3 × 1 matrix 1 a.

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A: Image is attached with detailed solution.

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A: The given differential equation ia,y'''-12y''+48y'-64y=12-32e-4t+2e4t

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.