Determine the coordinates tm ym of the maximum point of the

Question

Solve the IVP with differential operator method:

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

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

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

Determine the behaviour of t_m and y_m as β→∞.