1) Solve :

$\displaystyle y' = \cos (x) - y\sin (x) + y^2

$

Know : $\displaystyle y = \sin (x)$ is the solution.

2 ) Solve :

$\displaystyle y' = 2 + \frac{1}{2}\left( {x - \frac{1}{x}} \right)y - \frac{1}{2}y^2

$

Know :

$\displaystyle y = x + \frac{1}{x}$ is the solution.