Differential Equations — NDA Mathematics PYQs

Consider the following for the two (02) items that follow :
The slope of the tangent to the curve $y=f(x)$ at $(x,f(x))$ is $4$ for every real number $x$ and the curve passes through the origin.

What is the nature of the curve?

What is the degree of the differential equation ${\left(\frac{d^{2}y}{d{x}^2}\right)}^3={\left(\frac{dy}{dx}\right)}^{5/2}$?

Consider the following statements :
I. $y=x{e}^{2x}$ is the solution of $\frac{dy}{dx}=y\left(2+\frac{1}{x}\right)$.
II. $y=x\ln |x|+cx$ is the solution of $\frac{dy}{dx}=\frac{x+y}{x}$.
Which of the statements given above is/are correct?

If $k$ is an arbitrary constant, then what is the general solution of the equation $(x+y{)}^2\frac{dy}{dx}=k^2$?