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 respectively :

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

Answer 1

Answer: (C)

$2,2$

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

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

$\Rightarrow x^4{\left(\frac{d^{2}y}{d{x}^2}\right)}^2={(1+{\left(\frac{dy}{dx}\right)}^2)}^3$, Square both sides

Hence degree $=2$ and order $=2$