Into which of the following systems can this homogeneous third-order differential equation be transformed?

A) $ x_{1}^{\prime}=x_{2}, x_{2}^{\prime}=x_{3}, x_{3}^{\prime}=-10 x_{3}-2 x_{2}-8 x_{1} $
B) $ x_{1}^{\prime}=x_{2}, x_{2}^{\prime}=x_{3}, x_{3}^{\prime}=\frac{10}{5 t} x_{3}+\frac{2}{5 t^{2}} x_{2}+\frac{8}{5 t^{3}} x_{1} $
C) $ x_{1^{\prime}}=x_{2}, x_{2}^{\prime}=x_{3}, x_{3}^{\prime}=10 x_{3}+2 x_{2}+8 x_{1} $
D) $ x_{1^{\prime}}^{\prime}=x_{2}, x_{2}^{\prime}=x_{3}, x_{3^{\prime}}^{\prime}=\frac{-10}{5 t} x_{3}-\frac{2}{5 t^{2}} x_{2}-\frac{8}{5 t^{3}} x_{1} $

Question

Into which of the following systems can this homogeneous third-order differential equation be transformed?

A) $ x_{1}^{\prime}=x_{2}, x_{2}^{\prime}=x_{3}, x_{3}^{\prime}=-10 x_{3}-2 x_{2}-8 x_{1} $ 
B) $ x_{1}^{\prime}=x_{2}, x_{2}^{\prime}=x_{3}, x_{3}^{\prime}=\frac{10}{5 t} x_{3}+\frac{2}{5 t^{2}} x_{2}+\frac{8}{5 t^{3}} x_{1} $ 
C) $ x_{1^{\prime}}=x_{2}, x_{2}^{\prime}=x_{3}, x_{3}^{\prime}=10 x_{3}+2 x_{2}+8 x_{1} $ 
D) $ x_{1^{\prime}}^{\prime}=x_{2}, x_{2}^{\prime}=x_{3}, x_{3^{\prime}}^{\prime}=\frac{-10}{5 t} x_{3}-\frac{2}{5 t^{2}} x_{2}-\frac{8}{5 t^{3}} x_{1} $

Quizplus · Accepted Answer

The Answer is D

Into Which of the Following Systems Can This Homogeneous Third-Order x1′=x2,x2′=x3,x3′=−10x3−2x2−8x1 x_{1}^{\prime}=x_{2}, x_{2}^{\prime}=x_{3}, x_{3}^{\prime}=-10 x_{3}-2 x_{2}-8 x_{1} x1′​=x2​,x2′​=x3​,x3′​=−10x3​−2x2​−8x1​

Into Which of the Following Systems Can This Homogeneous Third-Order $x_{1}^{\prime}=x_{2}, x_{2}^{\prime}=x_{3}, x_{3}^{\prime}=-10 x_{3}-2 x_{2}-8 x_{1}$