Originally Posted by

**mollymcf2009** **PLEASE don't solve this, I just want to know if my process is correct. Thanks!

Which of the following functions are solutions of the differential equation:

$\displaystyle y'' + y = sin(x)$?

a) $\displaystyle y = sin(x)$

b) $\displaystyle y = xsin(x) - 8xcos(x)$

c) $\displaystyle y = -\frac{1}{2}xcos(x)$

d) $\displaystyle y = cos(x)$

e) $\displaystyle y = \frac{1}{2}xsin(x)$

Just want to make sure I'm doing this correctly.

First, I get y'' of each of these. Plug y'' & y into the DE and simplify without moving anything to different sides of the equation. Then if whatever is on the left ends up = sin(x) then it IS a solution. Is this the right way to do this?

Thanks!