Question

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

• A. 2, 1
• B. 2, 3
• C. 2, 2
• D. 2, 6

Answer 1

The correct option is C 2, 2

Simplify the differential equation $x^2=\frac{{(1+{\left(\frac{dy}{dx}\right)}^2)}^{3/2}}{\frac{d^{2}y}{d{x}^2}}$
$\Rightarrow x^2\frac{d^{2}y}{d{x}^2}={(1+{\left(\frac{dy}{dx}\right)}^2)}^{3/2}$
Squaring both side
$\Rightarrow x^4{\left(\frac{d^{2}y}{d{x}^2}\right)}^2={(1+{\left(\frac{dy}{dx}\right)}^2)}^3$
As, Order of a differential equation is the order of the highest order derivate and the degree of differential equation is represented by the power of the highest order derivative in the given differential equation.
Hence, Order=2 and degree =2