Consider the following for the next items that follow:

A parabola passes through (1, 2) and satisfies the differential equation $\frac{d y}{d x}=\frac{2 y}{x}, x>0, y>0 .$

What is the length of latus rectum of the parabola?

What are the order and the degree respectively of the differential equation $\rm x^2\left(\frac{d^3 y}{d x^3}\right)^2+\left(\frac{d y}{d x}\right)^4+\sin x=0$ ? 

What is the differential equation of all parabolas of the type y2 = 4a (x - b)?

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 order of the differential equation ?