first order ODE

For the exact differential equation, $\frac{du}{dx}=\frac{-xu^2}{2+x^2u}$ which one of the following is the solution?

Consider the following differential equation $${{dy} \over {dt}} = - 5y;$$ initial condition: $$y=2$$ at $$t=0.$$ The value of $$y$$ at $$t=3$$ is

The general solution of the differential equation $$\,\,{{dy} \over {dx}} = \cos \left( {x + y} \right),\,\,$$ with $$c$$ as a constant, is

The solution of the initial value problem $$\,\,{{dy} \over {dx}} = - 2xy;y\left( 0 \right) = 2\,\,\,$$ is

The solution of $${{d\,y} \over {d\,x}} = {y^2}$$ with initial value $$y(0)=1$$ is bounded in the interval is

The solution of the differential equation $${{dy} \over {dx}} + {y^2} = 0$$ is