The solution of the differential equation $\frac{d y}{d x}=\frac{x+2 y}{x}$ is $x+y=k x^2$.

Solution of $\frac{x d y}{d x}=y+x \tan \frac{y}{x}$ is $\sin \left(\frac{y}{x}\right)=c x$

The differential equation of all non horizontal lines in a plane is $\frac{d^2 x}{d y^2}=0$