Question

The complementary solution for the homogeneous equation y'' + 2y' + y = 0 winll be given as

Answer 1

$$y''+2y'+y=0$$

Corresponding (auxiliary) equation

$$r^2+2r+1=0$$

$$(r+1)^2=0$$

$$r_1=r_2=-1$$

The complementary solution is

$$y_c=c_1e^{-t}+c_2te^{-t}$$