Which of the following functions y = f(x) satisfy y' = - $\frac { 2 } { 3 }$ y, f(1) = 1?
(I) y = $e ^ { x }$
(II) y = $e ^ { - 2 / 3 x }$
(III) y = $\mathrm { e } ^ { ( - 2 / 3 ) ( x - 1 ) }$ (IV) y = - $\frac { 2 } { 3 }$ $e ^ { x }$
A) III only
B) I and II
C) IV only
D) II only
E) none of these

Question

Which of the following functions y = f(x) satisfy y' = - $\frac { 2 } { 3 }$ y, f(1) = 1? 
(I) y = $e ^ { x }$ 
(II) y = $e ^ { - 2 / 3 x }$ 
(III) y = $\mathrm { e } ^ { ( - 2 / 3 ) ( x - 1 ) }$ (IV) y = - $\frac { 2 } { 3 }$ $e ^ { x }$
A) III only
B) I and II
C) IV only
D) II only
E) none of these

Quizplus · Accepted Answer

The differential equation y' = - (2/3)y has the solution y = Ce^(-2/3)x. Given f(1) = 1, we find C = e^(2/3). Thus, y = e^(2/3)e^(-2/3)x = e^(-2/3(x-1)), which matches option III.

Which of the Following Functions Y = F(x) Satisfy Y 23\frac { 2 } { 3 }32​

Which of the Following Functions Y = F(x) Satisfy Y $\frac { 2 } { 3 }$