Toronto Math Forum
MAT2442019F => MAT244Test & Quizzes => Quiz3 => Topic started by: yueyangyu on October 11, 2019, 02:00:02 PM

Find the general solution of the given differential equation.
$$y''2y'2y=0$$
Assume that $$y=e^{rt}$$ and it follows that r must be a root of characteristic equation
$$r^22r2=0$$
$$r=\frac{b\pm\sqrt{b^24ac}}{2a}$$
Then,
$$r_1=1+\sqrt{3} \quad r_2=1\sqrt{3}$$
Therefore, the general solution of the given differential equation is:
$$y=c_1e^{(1+\sqrt{3})t}+c_2e^{(1\sqrt{3})t}$$