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# 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(-infty,+inftyright)}.{y}text{}+{2}{y}'+{y}={0}

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Second order linear equations asked 2020-12-24
Linear equations of second order with constant coefficients.
Find all solutions on
$${\left(-\infty,+\infty\right)}.{y}\text{}+{2}{y}'+{y}={0}$$

## Answers (1) 2020-12-25
The characteristic equation is given by
$${r}^{2}+{2}{r}+{1}={0}$$
and has the roots $$r_1=11 and r_2=1$$.
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.

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