Question

 Find the general solution of the equation y^''− 4y^'+ 4y = 0. 

Answer 1

The auxiliary equation is

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

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

$$r_1=r_2=2$$

The general solution of the equation

$$y=c_1e^{2t}+c_2te^{2t}$$