Consider the following statements in respect of the differential equation $\frac{d^{2}y}{d{x}^2}+\cos \left(\frac{dy}{dx}\right)=0$

$\mathrm{I}$. The degree of the differential equation is not defined.

$\mathrm{II}$. The order of the differential equation is $2$.

Which of the above statement$\left(\text{s}\right)$ is $/$are correct $?$

What is the solution of the equation $\ln \left(\frac{dy}{dx}\right)+x=0,$ where $C$ is an arbitrary constant.

What is the solution of the differential equation $\sin \left(\frac{dy}{dx}\right)-a=0$, where $C$ is an arbitrary constant $?$

What is the solution of the differential equation $\frac{ydx-xdy}{y^2}=0$, where $C$ is an arbitrary constant $?$

What is the solution of the differential equation $\frac{dx}{dy}+\frac{x}{y}-y^2=0$, where $C$ is an arbitrary constant $?$

Consider the following statements

$\mathrm{I}$. The general solution of $\frac{dy}{dx}=f\left(x\right)+x$ is of the form $y=g\left(x\right)+C,$ where $C$ is an arbitrary constant.

$\mathrm{II}$. The degree of ${\left(\frac{dy}{dx}\right)}^2=f\left(x\right)$ is $2$

Which of the above statement $\left(\mathrm{s}\right)$ is$/$are correct $?$