The differential equation of all parabolas wh | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The general equation of a parabola with its axis parallel to the $Y$-axis is given by $y = Ax^2 + Bx + C$,where $A, B, C$ are arbitrary constants.

Vedclass · Accepted Answer

$\frac{d^3 y}{d x^3}=0$

Vedclass · Answer

(A) The general equation of a parabola with its axis parallel to the $Y$-axis is given by $y = Ax^2 + Bx + C$,where $A, B, C$ are arbitrary constants.To find the differential equation,we differentiate with respect to $x$ three times to eliminate the three constants.First derivative: $\frac{dy}{dx} = 2Ax + B$.Second derivative: $\frac{d^2y}{dx^2} = 2A$.Third derivative: $\frac{d^3y}{dx^3} = 0$.Thus,the required differential equation is $\frac{d^3y}{dx^3} = 0$.

The differential equation of all parabolas whose axes are parallel to the $Y$-axis is:

Similar Questions

$y = 4\sin 3x$ is a solution of the differential equation

The differential equation representing the family of parabolas having vertex at the origin and axis along the positive $Y$-axis is

The differential equation for which $\sqrt{1+y^2}=C x e^{\tan ^{-1} x}$ is the general solution,is

The differential equation of the family of parabolas with vertex at $(0,-1)$ and having axis along the $Y$-axis is

The differential equation of the circles having their centres on the line $y=8$ and touching the $X$-axis is

Vedclass Test Series

Exam Paper Generator

Online Exam Module