Suppose differentiable functions and satisfy dx dt =5y

MATHEMATICS · Single correct · AP · Physics C: Mechanics · Linear Momentum · Linear Momentum

Problem

Suppose differentiable functions

x(t)

and

y(t)

satisfy

\frac{dx}{dt}=5y, \qquad \frac{dy}{dt}=-5x

for all

t

. Which of the following second-order differential equations involving only

x

must be true? (a)

\displaystyle\frac{d^{2}x}{dt^{2}}=-x

(b)

\displaystyle\frac{d^{2}x}{dt^{2}}=-25x

(c)

\displaystyle\frac{d^{2}x}{dt^{2}}=25x

(d)

\displaystyle\frac{d^{2}x}{dt^{2}}=-5x