Which of the following is a solution of the differential equation $\frac { d ^ { 2 } y } { d x ^ { 2 } } + 4 y = 0$
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 $\frac { d ^ { 2 } y } { d x ^ { 2 } } + 4 y = 0$ 
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 second-order linear homogeneous differential equation with constant coefficients. The characteristic equation of this differential equation is $r^2 + 4 = 0$, which has roots $r = \pm 2i$. The general solution to this differential equation is $y = C_1 \cos(2x) + C_2 \sin(2x)$, where $C_1$ and $C_2$ are constants. Among the given options, only $y = \sin(2x)$ matches this form.

Which of the Following Is a Solution of the Differential d2ydx2+4y=0\frac { d ^ { 2 } y } { d x ^ { 2 } } + 4 y = 0dx2d2y​+4y=0

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