Question

Find the order and degree of $\frac{d^{2}y}{d{x}^2}={[1+{\left(\frac{dy}{dx}\right)}^2]}^{3/2}$

• A. $1,2$
• B. $2,2$
• C. $2,\frac{3}{2}$
• D. $\frac{3}{2},2$

Answer 1

Answer: (B)

$2,2$

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

Squaring both sides, we get

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

Order: Order of a differential equation is the order of the highest order derivative (also known as differential coefficient) present in the equation

Degree: The degree of the differential equation is represented by the power of the highest order derivative in the given differential equation.

Hence the degree of the given differential is $2$ and the order is also $2.$