# The order and degree of the differential equation $\bigg[1+\bigg(\large\frac{dy}{dx}\bigg)^2\bigg]=\bigg(\large\frac{d^2y}{dx^2}\bigg)$ are

:$(A)\;2,\frac{3}{2}\quad(B)\;2,3\quad(C)\;2,1\quad(D)\;3,4$

Toolbox:
• Degree of the differential equation is the power of the highest order differential coefficient.
The given equation is $\bigg[1+\bigg(\large\frac{dy}{dx}\bigg)^2\bigg]=\bigg(\large\frac{d^2y}{dx^2}\bigg)$
The highest order of the equation is $\large\frac{d^2y}{dx^2}$ which is 2.
Hence the order of the equation is $2$
The power of the highest order differential coefficient is $1$
So its degree is $1$
Clearly the above equation is a non-linear differential equation of order $2$ and degree $1$
Hence the correct option is $C$