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**charikaar** $\displaystyle y^{(n)} + p_{n-1}(x)\,y^{(n-1)} + \cdots + p_1(x)\,y' + p_0(x)\,y = 0,$ (1) be the n-th order homogeneous differential equation which is represented in matrix form $\displaystyle \dot{\vec{y}} = A \vec{y}$ (2)

If $\displaystyle y_1,...,y_n$ are the solutions to (1), what are the correspondence solutions of (2).

I know if $\displaystyle y$ is solution to (1) then the corresponding solution $\displaystyle \vec{y}$for (2) is given the vector (y,y',y'',y''',......y^n-1)^T

Thank you for your help in advance.