GATE BT 2025 | Question: 35

Question

​​Let $m$ and $n$ be fixed real numbers. If the function $y(t)=C_{1} e^{t}+C_{2} e^{-t}$ is a solution of
$$ \frac{d^{2} y}{d t^{2}}+m \frac{d y}{d t}+n y=0$$
for any constants $C_{1}$ and $C_{2}$, then $m+n$ is equal to

• A. $-2$
• B. $-1$
• C. $0$
• D. $1$