The solution of $$y' = \sqrt{xy}$$ with initial value $$y(1)=0$$ is given by

The solution of $$y^2-xy'=0$$ with initial value $$y(1)=1$$ is given by

The solution of $$y' (\sin{x})y = 0$$ with initial value $$y(\pi/2)=1$$ is given by