Consider the following for the next two (02) items that follow :

Suppose E is the differential equation representing family of curves y² = 2cx + 2c√c where c is a positive parameter.  

What is the degree of the differential equation ? 

A solution of the differential equation

$\left(\frac{d y}{d x}\right)^2-x \frac{d y}{d x}=0 $ is

Consider the following statements:

1. The degree of the differential equation $\frac{\text{dy}}{\text{dx}} + \cos \left(\frac{\text{dy}}{\text{dx}}\right)$ = 0 is 1.

2. The order of the differential equation $\left(\frac{\text{d}^2\text{y}}{\text{dx}^2}\right)^3 + \cos \left(\frac{\text{dy}}{\text{dx}}\right) $ = 0 is 2.

Which of the statements above is/are correct?

What is the differential equation of the family of parabolas having a vertex at origin and axis along positive y-axis?