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.

sine

step-by-step explanation:

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11