Question

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

• A. $3$ and $7$
• B. $3$ and $2$
• C. $7$ and $3$
• D. $2$ and $3$

Answer 1

Answer: (B)

$3$ and $2$

First we have to raise both equations with power of $3$ to make all the powers, integer, we get

${[1+(\frac{dy}{dx}{)}^{\frac{3}{}}]}^7=7{\left(\frac{d^{2}y}{d{x}^2}\right)}^3$

The degree of a differential equation is represented by the power of the highest order derivative in the given differential equation. So here the degree is $3$.

Order of a differential equation is the order of the highest order derivative present in the equation. So here the order is $2$.