Question

Find the order and degree of the differential equation:

$\sqrt{1+{\left(\frac{dy}{dx}\right)}^2}=1+x$.

Answer 1

Given the differential equation is,

$\sqrt{1+{\left(\frac{dy}{dx}\right)}^2}=1+x$

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

From this equation it is clear that the highest ordered term involved in the equation is first order term so order of the differential equation is $1$ and power of that term is $2$ so the degree of the equation is $2$.