MAT244-2018S > Quiz-3

Q3-T0201

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Victor Ivrii:
Find the general solution of the given differential equation.
$$y'' + 3y' + 2y = 0.$$

Darren Zhang:
Let y = e^{rt},
Substitution of the assumed solution results in the characteristic equation $$r^2+3r+2=0$$
The roots of the equation are r = -2, -1 . Hence the general solution is $y = c_{1}e^{-t}+c_{2}e^{-2t}$

Meng Wu:
$$y’’+3y’+2y=0$$
We assume that $y=e^{rt}$, and then it follows that $r$ must be a root of characteristic equation $$r^2+3r+2=(r+1)(r+2)=0$$
$$\cases{r_1=-1\\r_2=-2}$$
Since the general solution has the form of $$y=c_1e^{r_1t}+c_2e^{r_2t}$$
Therefore, the general solution of the given differential equation is
$$y=c_1e^{-t}+c_2e^{-2t}$$

Victor Ivrii:
Meng Wu,
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