Which of the following are solutions to the homogeneous second-order differential equation ?
Select all that apply.
A) $ y_{1}=8 e^{-2 t}+2 e^{2 t} $
B) $ y_{2}=\mathrm{Ce}^{-2 t} $, where $ \mathrm{C} $ is any real constant
C) $ y_{3}=8\left(e^{2 t}+e^{-2 t}\right) $
D) $ y_{4}=C e^{2 t} $, where $ C $ is any real constant
E) $ y_{5}=\left(C_{1} e^{2 t}\right) \cdot\left(C_{2} e^{-2 t}\right) $, where $ C_{1} $ and $ C_{2} $ are any real constants
F) $ y_{6}=2 e^{-2 t} $
G) $ y_{7}=C\left(e^{-2 t}+e^{2 t}\right) $, where $ C $ is any real constant

Question

Which of the following are solutions to the homogeneous second-order differential equation  ? 
Select all that apply.
A) $ y_{1}=8 e^{-2 t}+2 e^{2 t} $ 
B) $ y_{2}=\mathrm{Ce}^{-2 t} $, where $ \mathrm{C} $ is any real constant 
C) $ y_{3}=8\left(e^{2 t}+e^{-2 t}\right) $ 
D) $ y_{4}=C e^{2 t} $, where $ C $ is any real constant 
E) $ y_{5}=\left(C_{1} e^{2 t}\right) \cdot\left(C_{2} e^{-2 t}\right) $, where $ C_{1} $ and $ C_{2} $ are any real constants 
F) $ y_{6}=2 e^{-2 t} $ 
G) $ y_{7}=C\left(e^{-2 t}+e^{2 t}\right) $, where $ C $ is any real constant

Quizplus · Accepted Answer

The Answer of Which of the following are solutions to the homogeneous second-order differential equation  ? 
Select all that apply.
A) $ y_{1}=8 e^{-2 t}+2 e^{2 t} $ 
B) $ y_{2}=\mathrm{Ce}^{-2 t} $, where $ \mathrm{C} $ is any real constant 
C) $ y_{3}=8\left(e^{2 t}+e^{-2 t}\right) $ 
D) $ y_{4}=C e^{2 t} $, where $ C $ is any real constant 
E) $ y_{5}=\left(C_{1} e^{2 t}\right) \cdot\left(C_{2} e^{-2 t}\right) $, where $ C_{1} $ and $ C_{2} $ are any real constants 
F) $ y_{6}=2 e^{-2 t} $ 
G) $ y_{7}=C\left(e^{-2 t}+e^{2 t}\right) $, where $ C $ is any real constant

Which of the Following Are Solutions to the Homogeneous Second-Order y1=8e−2t+2e2t y_{1}=8 e^{-2 t}+2 e^{2 t} y1​=8e−2t+2e2t

Which of the Following Are Solutions to the Homogeneous Second-Order $y_{1}=8 e^{-2 t}+2 e^{2 t}$