How to find the general solution for this ODE? I'm really stuck on how to go about solving the following first order ODE; I've got little idea on how to approach it, and I'd really appreciate if someone could give me some hints and/or working for a solution so I can have a reference point on how to approach these sorts of problems.
The following is one of many ODE's I've gotten off a problem set I found in a textbook at a library:
$$y' = xe^{-\sin(x)} - y\cos(x)$$
Can anyone help?

The particular solution is
$$y=\frac{1}{2}x^2 e^{-\sin x}$$
Then solve for the homogeneous solution.
Can you take it from here?
