Which of the following functions satisfy the differential equation y' = -8y?
(I) y = - $e ^ { - 8 x }$
(II) y = $e ^ { - 4 x }$ + 3
(III) y = 5 $e ^ { - 4 x }$ (IV) y = 6 $e ^ { - 8 x }$
A) II and III
B) I and IV
C) II only
D) III only
E) none of these

Question

Which of the following functions satisfy the differential equation y' = -8y? 
(I) y = - $e ^ { - 8 x }$ 
(II) y = $e ^ { - 4 x }$ + 3
(III) y = 5 $e ^ { - 4 x }$ (IV) y = 6 $e ^ { - 8 x }$
A) II and III
B) I and IV
C) II only
D) III only
E) none of these

Quizplus · Accepted Answer

To satisfy the differential equation y' = -8y, when we differentiate the given functions, the derivative should equal -8 times the original function. For (I) $y = -e^{-8x}$, $y' = 8e^{-8x}$ which does not match. For (II) $y = e^{-4x} + 3$, $y' = -4e^{-4x}$ which does not match. For (III) $y = 5e^{-4x}$, $y' = -20e^{-4x}$ which does not match. For (IV) $y = 6e^{-8x}$, $y' = -48e^{-8x} = -8(6e^{-8x})$, which matches. Thus, only (I) and (IV) satisfy the differential equation.

Which of the Following Functions Satisfy the Differential Equation Y e−8xe ^ { - 8 x }e−8x

Which of the Following Functions Satisfy the Differential Equation Y $e ^ { - 8 x }$