The family , with independent constants and , is given. What is the lowest-order…

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

The family

y = C_{1}\cos x + C_{2}\sin x

, with independent constants

C_{1}

and

C_{2}

, is given. What is the lowest-order differential equation whose solution set consists exactly of this family? (a)

y'' - y = 0

(b)

y' + y = 0

(c)

y'' + y = 0

(d)

y'' + 2y = 0