Question

y'' + 14y' + 49y = 0

Answer 1

Let us solve the characteristic equation of the differential equation $y'' + 14y' + 49y = 0$ :

$k^2+14k+49=0$

$(k+7)^2=0$

It follows that $k_1=k_2=-7$.

Therefore, the solution of the differential equation $y'' + 14y' + 49y = 0$ is the following:

$y=(C_1+C_2x)e^{-7x}$