The order and degree of the differential equa | vedclass

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

Question

(A) Given differential equation is $\sqrt{\frac{dy}{dx}} - 4\frac{dy}{dx} - 7x = 0$. Rearranging the terms,we get $\sqrt{\frac{dy}{dx}} = 4\frac{dy}{d

Vedclass · Accepted Answer

$1, 2$

Vedclass · Answer

(A) Given differential equation is $\sqrt{\frac{dy}{dx}} - 4\frac{dy}{dx} - 7x = 0$. Rearranging the terms,we get $\sqrt{\frac{dy}{dx}} = 4\frac{dy}{dx} + 7x$. Squaring both sides to eliminate the square root,we get $\frac{dy}{dx} = (4\frac{dy}{dx} + 7x)^2$. Expanding the right side,$\frac{dy}{dx} = 16(\frac{dy}{dx})^2 + 56x\frac{dy}{dx} + 49x^2$. The highest order derivative present is $\frac{dy}{dx}$,so the order is $1$. The highest power of the highest order derivative after making the equation a polynomial in derivatives is $2$. Therefore,the order is $1$ and the degree is $2$.

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

Similar Questions

The order and degree of the differential equation of all tangent lines to the parabola $x^2 = 4y$ are respectively:

The order and degree of the differential equation $\sqrt[3]{\frac{d^2 y}{d x^2}}=\sqrt{\frac{d^3 y}{d x^3}}$ are . . . . . . and . . . . . . .

The sum of the degree and order of the differential equation $\sqrt{\frac{d^2 y}{d x^2}}=\sqrt[5]{\frac{dy}{d x}-5}$ is

The degree of the differential equation $\frac{d^2 y}{d x^2}+3\left(\frac{d y}{d x}\right)^2=x^2 \log \left(\frac{d^2 y}{d x^2}\right)$ is

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module