Question

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

• A. $2,2$
• B. $2,3$
• C. $2,1$
• D. None of these

Answer 1

The correct option is A $2,2$

$\rho =\frac{{[1+{\left(\frac{dy}{dx}\right)}^2]}^{\frac{3}{2}}}{\frac{d^{2}y}{d{x}^2}}$
$\Rightarrow \rho \left(\frac{d^{2}y}{d{x}^2}\right)={[1+{\left(\frac{dy}{dx}\right)}^2]}^{3/2}$
On squaring both sides, we get
$\Rightarrow {\rho }^2{\left(\frac{d^{2}y}{d{x}^2}\right)}^2={[1+{\left(\frac{dy}{dx}\right)}^2]}^3$
Clearly, it is a second order differential equation of degree 2.

Hence, the answer is $2,2$.