### Author Topic: TUT0602 QUIZ 4  (Read 550 times)

#### Fenglun Wu

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##### TUT0602 QUIZ 4
« on: October 18, 2019, 03:30:57 PM »
Find the general solution of the given differential equation.
$$y'' + 2y' + 2y = 0$$

Solve the equation $r^2+2r+2=0$ for $r$
$$r = \frac{-2 \pm \sqrt{2^2-4(1)(2)} }{2(1)}$$
$$= \frac{-2 \pm \sqrt{-4}}{2} = \frac {-2 \pm 2i}{2} = -1 \pm i$$

We know that $y = c_1e^{\lambda t}cos(\mu t) + c_2e^{\lambda t}sin(\mu t)$ and $\lambda = -1$ and $\mu = 1$

Therefore, the required general solution is
$$y = c_1e^{-t}cos(t) + c_2e^{-t}sin(t)$$