Tazmin Horton

2021-02-21

Linear equations of second order with constant coefficients.
Find all solutions on
$\left(-\mathrm{\infty },+\mathrm{\infty }\right).y-2{y}^{\prime }+5y=0$

### Answer & Explanation

gotovub

The characteristic equation is given by
${r}^{2}+2r+5=0$
and has the roots ${r}_{1}=1+2i$ and ${r}_{2}=1-2i.$
The general solution is given by
$y={e}^{x}\left({c}_{1}\mathrm{cos}2x+{c}_{2}\mathrm{sin}2x\right)$, where are arbitracy constant.
This differential equation has infinitely many solutions since there is no initial conditions to determine a particular solution.

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