Question

Consider the differential equation:

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

Find order and degree.

Answer 1

Given the differential equation,

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

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

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

From the above equation it quite clear that the order of the differential equation is $2$ and degree is also $2$.