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}

Question
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.
0

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