Destinee Hensley
2022-03-25
Answered

Find the general solution of the given second-order differential equations

$2y{}^{\u2033}+2{y}^{\prime}+y=0$

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enriuadaziaa

Answered 2022-03-26
Author has **7** answers

Given differentia equation, $2y{}^{\u2033}+2{y}^{\prime}+y=0$

Auxilliary equation

$2{m}^{2}+2m+1=0$

Using quadratic formula,

$m=\frac{-2\pm \sqrt{{2}^{2}-4\left(2\right)\left(1\right)}}{2\left(2\right)}$

$m=\frac{-2\pm \sqrt{-4}}{4}$

$m=-\frac{1}{2}\pm \frac{1}{2}i$

So, the general solution:$y={c}_{1}\mathrm{cos}\left(\frac{1}{2}x\right)+{c}_{2}\mathrm{sin}\left(\frac{1}{2}x\right){e}^{-\frac{1}{2}x}$

Auxilliary equation

Using quadratic formula,

So, the general solution:

Jeffrey Jordon

Answered 2022-03-31
Author has **2262** answers

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