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

C

Step-by-step 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.