# (b) y''+y′+3⋅a5y=0

$\left(b\right)y+y\prime +3.25=0$

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avortarF

The characteristic equation of this Differential equations is ${r}^{2}+r+3.25=0$
Solve this quadratic equation: $r=\frac{-1±\sqrt{1-13}}{2}=\frac{-1±\sqrt{12}}{2}=\frac{-1±2i\sqrt{3}}{2}=-\left(\frac{1}{2}\right)±i\sqrt{3}$
Therefore, the solution is $y={C}_{1}\left(\frac{{e}^{-x}}{2}\right)\mathrm{cos}\left(x\sqrt{3}\right)+{C}_{2}\left(\frac{{e}^{-x}}{2}\right)\mathrm{sin}\left(x\sqrt{3}\right)$