MAT244-2018S > Quiz-3

Q3-T0501

(1/1)

**Victor Ivrii**:

Find the general solution of the given differential equation.

$$

2y'' - 3y' + y = 0.

$$

**Darren Zhang**:

Substitution of the assumed solution $y=e^{rt}$ results in the characteristic equation $$2r^2-3r+1=0$$

The roots of the equation are $r = \frac{1}{2}, 1$. Hence the general solution is $y = c_{1}e^{\frac{t}{2}}+c_{2}e^{\frac{3t}{2}}$

**Meng Wu**:

$$2y’’-3y’+y=0$$

We assume that $y=e^{rt}$, and then it follows that $r$ must be a root of characteristic equation $$2r^2-3r+1=(2r-1)(r-1)=0$$

Hence,

$$\cases{r_1={1\over2}\\r_2=1}$$

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

$$y=c_1e^{{1\over2}t}+c_2e^{t}$$

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