The solution of the system of differential equations in the previous problem is
A) $x = c _ { 1 } e ^ { - 0.3 t } , y = - 3 c _ { 1 } e ^ { - 03 t } + c _ { 2 } e ^ { - 02 t } , z = c _ { 3 } - 3 c _ { 1 } e ^ { - 0.3 t } - c _ { 2 } e ^ { - 0.2 t }$.

B) $x = c _ { 1 } e ^ { - 02 t } , y = - 2 c _ { 1 } e ^ { - 0.2 t } + c _ { 2 } e ^ { - 0.3 t } , z = c _ { 3 } + 2 c _ { 1 } e ^ { - 0.3 t } - c _ { 2 } e ^ { - 0.2 t }$ .

C) $x = c _ { 1 } e ^ { - 0.3 t } , y = - 3 c _ { 1 } e ^ { - 03 t } + c _ { 2 } e ^ { - 02 t } , z = c _ { 3 } + 2 c _ { 1 } e ^ { - 0.3 t } + c _ { 2 } e ^ { - 0.2 t }$

D) $x = c _ { 1 } e ^ { - 0.3 t } , y = - 3 c _ { 1 } e ^ { - 03 t } + c _ { 2 } e ^ { - 02 t } , z = c _ { 3 } + 2 c _ { 1 } e ^ { - 0.3 t } - c _ { 2 } e ^ { - 0.2 t }$.

E) $x = c _ { 1 } e ^ { - 02 t } , y = - 2 c _ { 1 } e ^ { - 0.2 t } + c _ { 2 } e ^ { - 0.3 t } , z = c _ { 3 } + 2 c _ { 1 } e ^ { - 0.3 t } - c _ { 2 } e ^ { - 0.2 t }$

Question

The solution of the system of differential equations in the previous problem is
A) $x = c _ { 1 } e ^ { - 0.3 t } , y = - 3 c _ { 1 } e ^ { - 03 t } + c _ { 2 } e ^ { - 02 t } , z = c _ { 3 } - 3 c _ { 1 } e ^ { - 0.3 t } - c _ { 2 } e ^ { - 0.2 t }$.

B) $x = c _ { 1 } e ^ { - 02 t } , y = - 2 c _ { 1 } e ^ { - 0.2 t } + c _ { 2 } e ^ { - 0.3 t } , z = c _ { 3 } + 2 c _ { 1 } e ^ { - 0.3 t } - c _ { 2 } e ^ { - 0.2 t }$ .

C) $x = c _ { 1 } e ^ { - 0.3 t } , y = - 3 c _ { 1 } e ^ { - 03 t } + c _ { 2 } e ^ { - 02 t } , z = c _ { 3 } + 2 c _ { 1 } e ^ { - 0.3 t } + c _ { 2 } e ^ { - 0.2 t }$

D) $x = c _ { 1 } e ^ { - 0.3 t } , y = - 3 c _ { 1 } e ^ { - 03 t } + c _ { 2 } e ^ { - 02 t } , z = c _ { 3 } + 2 c _ { 1 } e ^ { - 0.3 t } - c _ { 2 } e ^ { - 0.2 t }$.

E) $x = c _ { 1 } e ^ { - 02 t } , y = - 2 c _ { 1 } e ^ { - 0.2 t } + c _ { 2 } e ^ { - 0.3 t } , z = c _ { 3 } + 2 c _ { 1 } e ^ { - 0.3 t } - c _ { 2 } e ^ { - 0.2 t }$

Quizplus · Accepted Answer

The correct solution must have consistent decay rates in the exponents for each variable (x, y, z) and their coefficients must correctly reflect the system's interactions as described. Choice D correctly matches the pattern of decay rates and the interaction between variables as indicated by the coefficients.

The Solution of the System of Differential Equations in the Previous