Consider the first-order homogeneous system of linear differential equations
= x
Which of these is a fundamental set of solutions for this system?
A) $ \left\{\begin{array}{ll}-\sin (6 t) & \cos (6 t) \ \cos (6 t) & \sin (6 t)\end{array}\right\} $
B) $ \left\{\begin{array}{ll}\sin (6 t) & -\cos (6 t) \ \cos (6 t) & \sin (6 t)\end{array}\right\} $
C) $ \left\{\begin{array}{ll}\sin (36 t) & -\cos (36 t) \ \cos (36 t) & \sin (36 t)\end{array}\right\} $
D) $ \left\{\begin{array}{ll}e^{6 t} & -e^{-6 t} \ e^{6 t} & e^{-6 t}\end{array}\right\} $
E) $ \left\{\begin{array}{ll}e^{6 t} & e^{-6 t} \ -e^{6 t}, & e^{-6 t}\end{array}\right\} $

Question

Consider the first-order homogeneous system of linear differential equations
 =  x
Which of these is a fundamental set of solutions for this system?
A) $ \left\{\begin{array}{ll}-\sin (6 t) & \cos (6 t) \ \cos (6 t) & \sin (6 t)\end{array}\right\} $ 
B) $ \left\{\begin{array}{ll}\sin (6 t) & -\cos (6 t) \ \cos (6 t) & \sin (6 t)\end{array}\right\} $ 
C) $ \left\{\begin{array}{ll}\sin (36 t) & -\cos (36 t) \ \cos (36 t) & \sin (36 t)\end{array}\right\} $ 
D) $ \left\{\begin{array}{ll}e^{6 t} & -e^{-6 t} \ e^{6 t} & e^{-6 t}\end{array}\right\} $ 
E) $ \left\{\begin{array}{ll}e^{6 t} & e^{-6 t} \ -e^{6 t}, & e^{-6 t}\end{array}\right\} $

Quizplus · Accepted Answer

The Answer of Consider the first-order homogeneous system of linear differential equations
 =  x
Which of these is a fundamental set of solutions for this system?
A) $ \left\{\begin{array}{ll}-\sin (6 t) & \cos (6 t) \ \cos (6 t) & \sin (6 t)\end{array}\right\} $ 
B) $ \left\{\begin{array}{ll}\sin (6 t) & -\cos (6 t) \ \cos (6 t) & \sin (6 t)\end{array}\right\} $ 
C) $ \left\{\begin{array}{ll}\sin (36 t) & -\cos (36 t) \ \cos (36 t) & \sin (36 t)\end{array}\right\} $ 
D) $ \left\{\begin{array}{ll}e^{6 t} & -e^{-6 t} \ e^{6 t} & e^{-6 t}\end{array}\right\} $ 
E) $ \left\{\begin{array}{ll}e^{6 t} & e^{-6 t} \ -e^{6 t}, & e^{-6 t}\end{array}\right\} $

Consider the First-Order Homogeneous System of Linear Differential Equations {−sin⁡(6t)cos⁡(6t)cos⁡(6t)sin⁡(6t)} \left\{\begin{array}{ll}-\sin (6 t) & \cos (6 t) \\ \cos (6 t) & \sin (6 t)\end{array}\right\} {−sin(6t)cos(6t)​cos(6t)sin(6t)​}

Consider the First-Order Homogeneous System of Linear Differential Equations
$\left\{\begin{array}{ll}-\sin (6 t) & \cos (6 t) \\ \cos (6 t) & \sin (6 t)\end{array}\right\}$