Which of the following equations is satisfied by the function $x = e ^ { 2 t }$ ?
A) $x ^ { \prime } - 2 t = 0$
B) $x ^ { \prime } - 4 x t = 0$
C) $x ^ { \prime \prime } + 4 x = 0$
D) $x ^ { \prime \prime } + x = 0$
E) $x ^ { \prime } - 4 x = 0$
F) $x ^ { \prime } + 4 x = 0$
G) $x ^ { \prime \prime } - 4 x = 0$
H) $x ^ { \prime \prime } - x = 0$

Question

Which of the following equations is satisfied by the function $x = e ^ { 2 t }$ ?
A) $x ^ { \prime } - 2 t = 0$ 
B) $x ^ { \prime } - 4 x t = 0$ 
C) $x ^ { \prime \prime } + 4 x = 0$ 
D) $x ^ { \prime \prime } + x = 0$ 
E) $x ^ { \prime } - 4 x = 0$ 
F) $x ^ { \prime } + 4 x = 0$ 
G) $x ^ { \prime \prime } - 4 x = 0$ 
H) $x ^ { \prime \prime } - x = 0$

Quizplus · Accepted Answer

The first derivative $x' = 2e^{2t}$ and the second derivative $x'' = 4e^{2t}$. Substituting into $x'' - 4x = 0$ gives $4e^{2t} - 4e^{2t} = 0$, which is satisfied.

Which of the Following Equations Is Satisfied by the Function x=e2tx = e ^ { 2 t }x=e2t

Which of the Following Equations Is Satisfied by the Function $x = e ^ { 2 t }$