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### Topics - Nuo Chen

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##### Quiz-4 / Quiz4 TUT5102
« on: October 18, 2019, 02:07:09 PM »
Find the general solution of the differential equation
$$16 y^{\prime \prime}+24 y^{\prime}+9 y=0$$

$$\begin{array}{l}{16 r^{2}+24 r+9=0} \\ {(4 r+3)^{2}=0} \\ {r_{1}=r_{2}=-\frac{3}{4}} \\ {\therefore y=c_{1} e^{-\frac{3}{4} t}+C_{2} t e^{-\frac{3}{4} t}}\end{array}$$

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##### Quiz-3 / TUT5102 Quiz2
« on: October 11, 2019, 02:00:19 PM »
Find the general solution of the given differential equation.
$$2 y^{\prime \prime}-3 y^{\prime}+y=0$$

$$\begin{array}{l}{\text { Assume } y=e^{r t}} \\ {\text { then } 2 r^{2}-3 r+1=0} \\ {\qquad(2 r-1)(r-1)=0} \\ {\qquad r_{1}=\frac{1}{2}, r_{2}=1}\end{array}$$

$\because$ The general solution follows the form
$$y=c_{1} e^{r_{1} t}+c_{2} e^{r_2 t}$$
$$\therefore \quad y=c_{1} e^{\frac{t}{2}}+c_{2} e^{t}$$

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##### Quiz-2 / TUT5103 Quiz2
« on: October 04, 2019, 03:07:13 PM »
This is my question and the answer.

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