Determine the coordinates tm ym of the maximum point of the, Mathematics

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Determine the coordinates tm ym of the maximum point of the

Solve the IVP with differential operator method:

[D² + 5D + 6I]y = 0, y(0) = 2, y'(0) = β > 0.

a. Determine the coordinates (t_m, y_m) of the maximum point of the solution as function of β.

b. Determine the smallest value of β for which y_m ≥ 4.

c. Determine the behavior of t_m and y_m as β→∞.

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