Which of the following is a solution of the differential equation $\frac { d y } { d x } + 4 y ^ { 2 } = 0$
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 $\frac { d y } { d x } + 4 y ^ { 2 } = 0$ 
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 separable. Rearranging, we get $\frac{dy}{dx} = -4y^2$. Integrating both sides with respect to their variables, we find a solution of the form $y = \frac{1}{4x + C}$, where $C$ is a constant. Among the given options, $y = \frac{1}{4x + 1}$ matches this form, indicating it is a solution to the differential equation.

Which of the Following Is a Solution of the Differential dydx+4y2=0\frac { d y } { d x } + 4 y ^ { 2 } = 0dxdy​+4y2=0

Which of the Following Is a Solution of the Differential $\frac { d y } { d x } + 4 y ^ { 2 } = 0$