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) Step $1$: Write the given equation: $\sqrt{1 + \frac{1}{(dy/dx)^2}} = (d^2y/dx^2)^{3/2}$.Step $2$: Simplify the expression inside the square root:

Vedclass · Accepted Answer

Order $2$, Degree $3$

Vedclass · Answer

(A) Step $1$: Write the given equation: $\sqrt{1 + \frac{1}{(dy/dx)^2}} = (d^2y/dx^2)^{3/2}$.Step $2$: Simplify the expression inside the square root: $\sqrt{\frac{(dy/dx)^2 + 1}{(dy/dx)^2}} = (d^2y/dx^2)^{3/2}$.Step $3$: This becomes $\frac{\sqrt{(dy/dx)^2 + 1}}{|dy/dx|} = (d^2y/dx^2)^{3/2}$.Step $4$: Square both sides to remove the square root on the right: $\frac{(dy/dx)^2 + 1}{(dy/dx)^2} = (d^2y/dx^2)^3$.Step $5$: Multiply by $(dy/dx)^2$ to clear the fraction: $(dy/dx)^2 + 1 = (d^2y/dx^2)^3 \cdot (dy/dx)^2$.Step $6$: The highest order derivative is $d^2y/dx^2$, so the order is $2$. The power of the highest order derivative is $3$, so the degree is $3$.

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

Similar Questions

The degree and order of the differential equation of the family of parabolas whose axis is the $X$-axis, are respectively

The degree and order of the differential equation $\left[1+\left(\frac{dy}{dx}\right)^3\right]^{\frac{7}{3}}=7\left(\frac{d^2y}{dx^2}\right)$ respectively are

If $m$ and $n$ are the order and degree of the differential equation $\left(y^{\prime \prime}\right)^{5}+4 \cdot \frac{\left(y^{\prime \prime}\right)^{3}}{y^{\prime \prime \prime}}+y^{\prime \prime \prime}=\sin x$,then:

The number of arbitrary constants that appear in the general solution of the differential equation $\left(\frac{d^4 y}{d x^4}+\frac{d^2 y}{d x^2}\right)^{3 / 2}=5 \frac{d^3 y}{d x^3}$ is

The order and degree of the differential equation $3 - (\frac{d^3y}{dx^3})^{7/3} = (\frac{dy}{dx})^5$ are respectively

Vedclass Test Series

Exam Paper Generator

Online Exam Module