Which of the following is a solution of the differential equation $\frac { d y } { d x } + 4 y = 0$
A) $y = e ^ { - 4 x }$
B) $y = 4 x$
C) $y = e ^ { 2 x ^ { 2 } }$
D) $y = \sin 2 x$
E) $y = e ^ { 2 x }$
F) $y = 2 x ^ { 2 }$
G) $y = \frac { 1 } { 4 x + 1 }$
H) $y = e ^ { 4 x }$

Question

Which of the following is a solution of the differential equation $\frac { d y } { d x } + 4 y = 0$ 
A) $y = e ^ { - 4 x }$ 
B) $y = 4 x$ 
C) $y = e ^ { 2 x ^ { 2 } }$ 
D) $y = \sin 2 x$ 
E) $y = e ^ { 2 x }$ 
F) $y = 2 x ^ { 2 }$ 
G) $y = \frac { 1 } { 4 x + 1 }$ 
H) $y = e ^ { 4 x }$

Quizplus · Accepted Answer

The given differential equation is a first-order linear homogeneous differential equation. The solution to this type of equation can be found using the integrating factor method, which in this case leads to a solution of the form $y = Ce^{-4x}$, where $C$ is a constant. Among the given options, only $y = e^{-4x}$ matches this form.

Which of the Following Is a Solution of the Differential dydx+4y=0\frac { d y } { d x } + 4 y = 0dxdy​+4y=0

Which of the Following Is a Solution of the Differential $\frac { d y } { d x } + 4 y = 0$