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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