Which of the following functions y = f(x) satisfy y'= 32y, f (0) = $\frac { 1 } { 2 }$ ?
(I) y = 32 $e ^ { 1 / 2 x }$
(II) y = $\mathrm { e } ^ { 16 x }$
(III) y = $\frac { 1 } { 2 }$ $e ^ { 32 x }$ (IV) y = $\frac { 1 } { 2 }$ $x ^ { 32 }$
A) I only
B) IV only
C) III only
D) I and II
E) none of these

Question

Which of the following functions y = f(x) satisfy y'= 32y, f (0) = $\frac { 1 } { 2 }$ ? 
(I) y = 32 $e ^ { 1 / 2 x }$ 
(II) y = $\mathrm { e } ^ { 16 x }$ 
(III) y = $\frac { 1 } { 2 }$ $e ^ { 32 x }$ (IV) y = $\frac { 1 } { 2 }$ $x ^ { 32 }$
A) I only
B) IV only
C) III only
D) I and II
E) none of these

Quizplus · Accepted Answer

The correct function is (III) y = $\frac { 1 } { 2 }$ $e ^ { 32 x }$. This function satisfies the differential equation y'= 32y, and when x = 0, y = $\frac { 1 } { 2 }$, which meets the initial condition.

Which of the Following Functions Y = F(x) Satisfy Y'= 12\frac { 1 } { 2 }21​

Which of the Following Functions Y = F(x) Satisfy Y'= $\frac { 1 } { 2 }$