Which of the following are solutions to the homogeneous second-order differential equation ?
Select all that apply.
A) $ y_{1}=e^{-\frac{3}{2} t}+e^{\frac{3}{2} t} $
B) $ y_{2}=-6 t e^{\frac{3}{2} t}+8 $
C) $ y_{3}=C_{1} e^{-\frac{3}{2} t}+C_{2} t e^{-\frac{3}{2} t} $, where $ C_{1} $ and $ C_{2} $ are arbitrary real constants
D) $ y_{4}=8 e^{\frac{3}{2} t} $
E) $ y_{5}=C e^{\frac{3}{2} t}+10 t e^{\frac{3}{2} t} $
F) $ y_{6}=2 e^{\frac{3}{2} t}+8 t e^{\frac{3}{2} t}+8 $42_00

Question

Which of the following are solutions to the homogeneous second-order differential equation  ?
 Select all that apply.
A) $ y_{1}=e^{-\frac{3}{2} t}+e^{\frac{3}{2} t} $ 
B) $ y_{2}=-6 t e^{\frac{3}{2} t}+8 $ 
C) $ y_{3}=C_{1} e^{-\frac{3}{2} t}+C_{2} t e^{-\frac{3}{2} t} $, where $ C_{1} $ and $ C_{2} $ are arbitrary real constants 
D) $ y_{4}=8 e^{\frac{3}{2} t} $ 
E) $ y_{5}=C e^{\frac{3}{2} t}+10 t e^{\frac{3}{2} t} $ 
F) $ y_{6}=2 e^{\frac{3}{2} t}+8 t e^{\frac{3}{2} t}+8 $42_00

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}=e^{-\frac{3}{2} t}+e^{\frac{3}{2} t} $ 
B) $ y_{2}=-6 t e^{\frac{3}{2} t}+8 $ 
C) $ y_{3}=C_{1} e^{-\frac{3}{2} t}+C_{2} t e^{-\frac{3}{2} t} $, where $ C_{1} $ and $ C_{2} $ are arbitrary real constants 
D) $ y_{4}=8 e^{\frac{3}{2} t} $ 
E) $ y_{5}=C e^{\frac{3}{2} t}+10 t e^{\frac{3}{2} t} $ 
F) $ y_{6}=2 e^{\frac{3}{2} t}+8 t e^{\frac{3}{2} t}+8 $42_00

Which of the Following Are Solutions to the Homogeneous Second-Order y1=e−32t+e32t y_{1}=e^{-\frac{3}{2} t}+e^{\frac{3}{2} t} y1​=e−23​t+e23​t

Which of the Following Are Solutions to the Homogeneous Second-Order $y_{1}=e^{-\frac{3}{2} t}+e^{\frac{3}{2} t}$