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

Options

A. ` (d^(3)y)/(dx^(3))= 0`
B. `(d^(2)x)/(dy^(2))=C`
C. ` (d^(3)y)/(dx^(3))+(d^(2)x)/(dy^(2))=0`
D. `(d^(2)y)/(dx^(2))+2(dy)/(dx)=C`

Answer

a

Explanation

The equation of a member of the family of parabolas having axis to Y - axis is
` y = Ax^(2) + Bx +C` ltbRgt ` rArr (dy)/(dx) = 2Ax + B`
` (d^(2)y)/(dx^(2)) = 2A rArr (d^(3)y)/(dx^(3))= 0`