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 $\frac{d y}{d x}=\left(\frac{y}{x}\right)^{1 / 3}$ is $y^{2 / 3}-x^{2 / 3}=c$

Differential equation representing the family of curves $y=e^x(A \cos x+B \sin x)$ is $\frac{d^2 y}{d x^2}-2 \frac{d y}{d x}+2 y=0$

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