Q. The order and degree of the differential equation $\rho = \frac{\left\lbrack 1 + \left( \frac{dy}{dx} \right)^{2} \right\rbrack^{3/2}}{\frac{d^{2}y}{dx^{2}}}$ are respectively
A) 2, 2
B) 2, 3
C) 2, 1
D) None of these
Explanation
(a)
The given equation can be rewritten as
$\rho \bullet \frac{d^{2}y}{dx^{2}} = \left\lbrack 1 + \left( \frac{dy}{dx} \right)^{2} \right\rbrack^{3/2}$
On squaring both sides, we get
$\left( \rho \bullet \frac{d^{2}y}{dx^{2}} \right) = \left\lbrack 1 + \left( \frac{dy}{dx} \right)^{2} \right\rbrack^{3}$
$\Rightarrow$ order = 2, degree = 2.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.