Author Topic: TUT0202 Quiz3  (Read 258 times)

Anyue Huang

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TUT0202 Quiz3
« on: October 11, 2019, 02:00:30 PM »
Find a differential equation whose general solution is $y=c_{1} e^{-t / 2}+c_{2} e^{-2 t}$.

Then $r_{1}=-\frac{1}{2}, r_{2}=-2$ are two roots of the characteristic equation of the required differential equation.

so the characteristic equation should look like
$$
\begin{aligned}\left(r+\frac{1}{2}\right)(r+2) &=0 \\(2 r+1)(r+2) &=0 \\ 2 r^{2}+5 r+2 &=0 \end{aligned}
$$

which corresponds to the DE

$$
2 y^{\prime \prime}+5 y^{\prime}+2 y=0
$$