The order of the differential equation of all | 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 of symmetry is along the $X$-axis is given by $y^2 = 4a(x - h)$,which can be rewritten as $y^2 = Ax

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) The general equation of a parabola whose axis of symmetry is along the $X$-axis is given by $y^2 = 4a(x - h)$,which can be rewritten as $y^2 = Ax + B$,where $A$ and $B$ are arbitrary constants.Since there are $2$ arbitrary constants,we need to differentiate the equation twice to eliminate them.First derivative: $2y \frac{dy}{dx} = A$.Second derivative: $2 \left( \left( \frac{dy}{dx} \right)^2 + y \frac{d^2y}{dx^2} \right) = 0$.Since the highest order derivative present in the differential equation is the second derivative,the order of the differential equation is $2$.

The order of the differential equation of all parabolas whose axis of symmetry is along the $X$-axis is:

Similar Questions

The differential equation of all circles which pass through the origin and whose centres lie on the $y$-axis is:

The order of the differential equation of the family of all concentric circles centered at $(h, k)$ is

$\tan ^{-1} x + \tan ^{-1} y = c$ is the general solution of the differential equation:

If $a$ and $b$ are arbitrary constants,then the differential equation corresponding to the family of curves given by $y=x[a \cos (\log x)+b \sin (\log x)]$ is

The differential equation of the family of lines having $x$-intercept as $a$ and $y$-intercept as $b$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module