Which of the following functions are solutions to the differential equation $\frac { d ^ { 2 } y } { d x ^ { 2 } } = - y$ ? (Mark all correct answers)
A) $y = \sin ( 8 x ) + \cos ( 8 x )$
B) $y = 8 \cos x - \sin x$
C) $y = e ^ { x / 8 }$
D) $y = e ^ { - x / 8 }$

Question

Quizplus · Accepted Answer

The differential equation $\frac { d ^ { 2 } y } { d x ^ { 2 } } = - y$ has solutions of the form $y = A \cos x + B \sin x$. Option B fits this form.

Which of the Following Functions Are Solutions to the Differential d2ydx2=−y\frac { d ^ { 2 } y } { d x ^ { 2 } } = - ydx2d2y​=−y

Which of the Following Functions Are Solutions to the Differential $\frac { d ^ { 2 } y } { d x ^ { 2 } } = - y$