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

Question

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

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}=C e^{-\frac{4}{3} t^{2}} $, where $ C $ is any real constant 
B) $ y_{2}=-4 e^{-\frac{4}{3} t}+3 e^{\frac{4}{3} t} $ 
C) $ y_{3}=C e^{\frac{3}{4} t} $, where $ C $ is any real constant 
D) $ y_{4}=C\left(e^{-\frac{4}{3} t}+e^{\frac{4}{3} t}\right) $, where $ C $ is any real constant 
E) $ y_{1}=3 e^{\frac{3}{4} t}+-4 e^{-\frac{3}{4} t} $ 
F) $ y_{6}=t e^{3} $

Which of the Following Are Solutions to the Homogeneous Second-Order y1=Ce−43t2 y_{1}=C e^{-\frac{4}{3} t^{2}} y1​=Ce−34​t2

Which of the Following Are Solutions to the Homogeneous Second-Order $y_{1}=C e^{-\frac{4}{3} t^{2}}$