Consider the following statements:

I. $y=xe^{2x}$ is the solution of $\frac{dy}{dx}=y(2+\frac{1}{x})$

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 $(x+y)^{2}\frac{dy}{dx}=k^{2}$

Direction : Consider the following for the items that follow :

Let ydx + (x - y³)dy = 0 be a differential equation.  

What are the order and degree respectively of the differential equation? 

Direction : Consider the following for the items that follow :

Let ydx + (x - y³)dy = 0 be a differential equation.  

What is the solution of the differential equation?