1. ## Differential Equations

**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:

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

a) $y = sin(x)$

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

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

d) $y = cos(x)$

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

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!

2. 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:

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

a) $y = sin(x)$

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

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

d) $y = cos(x)$

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

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!
yes