Which equation does the function $y = e ^ { - 3 t }$ satisfy?
A) $y ^ { \prime \prime } - y ^ { \prime } + 12 y = 0$
B) $y ^ { \prime \prime } + y ^ { \prime } - 12 y = 0$
C) $y ^ { \prime \prime } + y ^ { \prime } + 12 y = 0$
D) $y ^ { \prime \prime } - 3 y ^ { \prime } + 12 y = 0$
E) $y ^ { \prime \prime } - y ^ { \prime } - 12 y = 0$

Question

Quizplus · Accepted Answer

We can take the first and second derivatives of $y = e ^ { - 3 t }$ as follows:

$$y' = -3e^{-3t}$$

$$y'' = 9e^{-3t}$$

Substituting these derivatives into each of the answer choices, we find that the only equation that satisfies the differential equation is:

$$y'' - y' - 12y = 0$$

which corresponds to answer choice E.

Which Equation Does the Function y=e−3ty = e ^ { - 3 t }y=e−3t

Which Equation Does the Function $y = e ^ { - 3 t }$