Question

Find the general solution of the following differential equations
y" +8y' + 16y = 0

Answer 1

Corresponding (auxiliary) equation

$$r^2+8r+16=0$$

$$(r+4)^2=0$$

$$r_1=r_2=-4$$

The general solution of the given differential equation is

$$y(t)=c_1e^{-4t}+c_2te^{-4t}$$