How do you find the vector-matrix form of the linear system corresponding to the higher order equation: y'' + a1 y' +a2 y = f

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How do you find the vector-matrix form of the linear system corresponding to the higher order equation: y'' + a1 y' +a2 y = f

Mathematics
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Just incase anyone wants to know how to solve this type of problem I figured out how: Start by reducing the the equation to a first order system by replacing y with x1, y' with x2 and y'' with x2'. Solve the equation for x2' (equals f-a1 x2- a2 x1). Notice that x1' = x2 =y' solve x'=Ax+b for A and b by using the two equations you derived for x1' and x2'. A should be a matrix [ 0 1] [-a2 -a1] b should be the matrix [0] [f]

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