Question

Which of the following functions are solutions of the differential equation y'' + y = 3 sin x? (select all that apply)

(a) y = 3sinx
(b) y = 3xsinx - 5xcosx
(c) y = -3 / 2xcosx
(d) y = 3cosx
(e) y = 3 / 2xsinx

Answer 1

C

Explanation:

We must compute the derivatives and check if the equation is satisfied.

A. . Differentiate again to get , then so this choice of y doesn't solve the equation.

B. and , then so y is not a solution

C. hence . Then so y is a solution.

D. and , then thus y isn't a solution

E. hence . Then then y is not a solution.