The order and degree of a differential equati | vedclass

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

Question

(A) Given the family of curves: $y^2 = 2C(x + \sqrt{C}) \quad \dots (i)$Differentiating with respect to $x$:$2y \frac{dy}{dx} = 2C$$\Rightarrow C = y

Vedclass · Accepted Answer

$1, 3$

Vedclass · Answer

(A) Given the family of curves: $y^2 = 2C(x + \sqrt{C}) \quad \dots (i)$Differentiating with respect to $x$:$2y \frac{dy}{dx} = 2C$$\Rightarrow C = y \frac{dy}{dx} \quad \dots (ii)$Substitute the value of $C$ from $(ii)$ into $(i)$:$y^2 = 2 \left( y \frac{dy}{dx} \right) \left( x + \sqrt{y \frac{dy}{dx}} \right)$$y = 2 \frac{dy}{dx} \left( x + \sqrt{y \frac{dy}{dx}} \right)$$y - 2x \frac{dy}{dx} = 2 \frac{dy}{dx} \sqrt{y \frac{dy}{dx}}$Squaring both sides:$(y - 2x \frac{dy}{dx})^2 = 4 \left( \frac{dy}{dx} \right)^2 \left( y \frac{dy}{dx} \right)$$(y - 2x \frac{dy}{dx})^2 = 4y \left( \frac{dy}{dx} \right)^3$The highest order derivative present is $\frac{dy}{dx}$,so the order is $1$.The power of the highest order derivative is $3$,so the degree is $3$.Thus,the order and degree are $1$ and $3$ respectively.

The order and degree of a differential equation obtained by eliminating the arbitrary constant $C$ from the family of curves $y^2 = 2C(x + \sqrt{C})$ are respectively:

Similar Questions

Which of the following equations is non-linear?

The order and degree of the differential equation $\sqrt{1 + \frac{1}{(dy/dx)^2}} = (d^2y/dx^2)^{3/2}$ are ...

The order and degree of the differential equation $\sqrt{\frac{dy}{dx}} - 4 \frac{dy}{dx} - 7x = 0$ are

If $m$ is the order and $n$ is the degree of the differential equation $y = \frac{dp}{dx} + \sqrt{a^2 p^2 - b^2}$,where $p = \frac{dy}{dx}$,then the value of $m+n$ is

If $y=a^3 e^{b^2 x+c}$ is the general solution of a differential equation,where $a$ and $c$ are arbitrary constants and $b$ is a fixed constant,then the order of the differential equation is

Vedclass Test Series

Exam Paper Generator

Online Exam Module