Differential Equations

If $$\cos\ y=x \cos(a+y)$$ then prove that:
$$\dfrac{dy}{dx}=\dfrac{\cos^{2}(a+y)}{\sin a}$$
The solution of $$ydx-xdy+\log {x}dx=0$$ is
The solution of $$ydx-xdy+\log {x}dx=0$$ is
The solution of $$ydx-xdy+\log {x}dx=0$$ is
The solution of $$ydx-xdy+\log {x}dx=0$$ is