The equation which represents the system of p | vedclass

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

Question

(A) The general equation of a parabola whose axis is 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 whose axis is 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.First derivative: $\frac{dy}{dx} = 2Ax + B$.Second derivative: $\frac{d^2y}{dx^2} = 2A$.Third derivative: $\frac{d^3y}{dx^3} = 0$.Since there are $3$ arbitrary constants, the order of the differential equation is $3$. Thus, the equation is $\frac{d^3y}{dx^3} = 0$.

The equation which represents the system of parabolas whose axis is parallel to the $y$-axis satisfies the differential equation:

Similar Questions

Let $p \in \mathbb{R}$. Then the differential equation of the family of curves $y=(\alpha+\beta x) e^{p x}$, where $\alpha$ and $\beta$ are arbitrary constants, is

If $k$ and $l$ respectively are the order and degree of the differential equation whose general solution represents the family of circles of constant radius, then $k^2+l^2=$

The differential equation whose solution represents the family $x^2 y = 4e^x + c$,where $c$ is an arbitrary constant,is

The differential equation for which $y^2 = 4a(x+a)$ (where $a$ is the parameter) is the general solution is:

If $m$ and $n$ are the order and degree of the differential equation of the family of parabolas with focus at the origin and $X$-axis as its axis, then $m n-m+n=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module