The differential equation of all parabolas whose axis are parallel to the y-axis is

Options

A. `(d^(3)y)/(dx^(3))=1`
B. `(d^(3)y)/(dx^(3))`
C. `(d^(3)y)/(dx^(3))=0`
D. none of these

Answer

C

Explanation

The equation of the parabola having their axes parallel to y-axis is given by
`y=ax^(2)+bx+c`
`rArr" "(dy)/(dx)=2ax+brArr(d^(2)y)/(dx^(2))=2arArr(d^(3)y)/(dx^(3))=0`
This is the required differential equation.