Correct substitution for the solution of the differential equation of the type $\frac{dy}{dx}=f\left(x,y\right)$, where $f\left(x,y\right)$ is a homogeneous function of zero degree is $y=vx$

Number of arbitrary constants in the particular solution of a differential equation of order two is two.

The differential equation representing the family of circles $x^2+(y-a{)}^2=a^2$ will be of order two.

The solution of the differential equation $\frac{dy}{dx}={\left(\frac{y}{x}\right)}^{\frac{1}{3}}$ is $y^{\frac{2}{3}}-x^{\frac{2}{3}}=C$, where $C$ is constant.

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

The solution of the differential equation $x\frac{dy}{dx}=y+x\tan \frac{y}{x}$ is $\sin \left(\frac{y}{x}\right)=cx$.

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