# Toronto Math Forum

## MAT244--2019F => MAT244--Test & Quizzes => Quiz-3 => Topic started by: Xinyu Jing on October 11, 2019, 08:06:25 PM

Title: QUIZ3 TUT 0502
Post by: Xinyu Jing on October 11, 2019, 08:06:25 PM
Question:Find the general solution of the given differential equation.
𝑦″−2𝑦′−2𝑦=0

Solution:
𝑦=$𝑒^{𝑟𝑡}$
and it follows that r must be a root of characteristic equation
$𝑟^{2}$−2𝑟−2=0

𝑟=$\frac{−𝑏±\sqrt{𝑏^{2}−4𝑎𝑐}}{2𝑎}$

$𝑟_{1}$=1+\sqrt{3} $𝑟_{2}$=1−\sqrt{3}

Therefore, the general solution of the given differential equation is:
𝑦=$C_{1}𝑒^{(1+\sqrt{3})𝑡}+C_{2}𝑒^{(1−\sqrt{3})𝑡}$