### Author Topic: quiz4 tut0502  (Read 570 times)

#### yueyangyu

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##### quiz4 tut0502
« on: October 18, 2019, 04:05:06 PM »
Find the general solution of the differential equation
$y''+2y'+2y=0$

The characteristic equation of the given equation is:

$r^2+2r+2=0$

$r=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-2\pm\sqrt{4-8}}{2}=-1\pm{i}$

Then,
$$r_1=-1+i \quad r_2=-1-i$$

Therefore, the general solution of the given differential equation is:
$$y=c_1e^{-t}cost+c_2e^{-t}sint$$