Solve the differential equation (D2 − 4D + 4)y = e2x + e⁻²x using D-operator methods.

Here are the general solutions for the given differential equations using D-operator methods.

1.1 $(D^2 - 4D + 4)y = e^{2x} + e^{-2x}$

Step 1: Find the complementary function ($y_c$).
The auxiliary equation is obtained by replacing $D$ with $m$:

$$m^2 - 4m + 4 = 0$$

This is a perfect square:

$$(m-2)^2 = 0$$

The roots are $m = 2$ (repeated root).
For repeated roots, the complementary function is of the form $y_c = (C_1 + C_2