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

$y=A e^x+B e^{-2 x}$ satisfies which of the following differential equations?

The differential equation corresponding to the family of curves given by $a x^2+b y^2=1$, where $a$ and $b$ are arbitrary constants, is:

Among the options given below,from which option can a differential equation of order two be formed?

The differential equation of all circles touching the $Y$-axis at the origin and having their center on the $X$-axis is:

The order of the differential equation whose solution is $y=a \cos x+b \sin x+c e^{-x}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module