# Linear equations of second order with constant coefficients. Find all solutions on {left(-infty,+inftyright)}.{y}text{}+{2}{y}'+{y}={0}

Linear equations of second order with constant coefficients.
Find all solutions on
$\left(-\mathrm{\infty },+\mathrm{\infty }\right).y+2{y}^{\prime }+y=0$
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Laaibah Pitt
The characteristic equation is given by
${r}^{2}+2r+1=0$
and has the roots ${r}_{1}=11and{r}_{2}=1$.
The general solution is given by
$y={e}^{x}\left({c}_{1}+{c}_{2}x\right)$, where c_1 and c_2 are arbitracy constant.