Question

Find degree and order of the differential equation.

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

Answer 1

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

On squaring both side we get,

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

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

$\Rightarrow x^2+2x\frac{dy}{dx}-1=0$

Order: Order of a differential equation is the order of the highest order derivative (also known as differential coefficient) present in the equation

Degree: The degree of the differential equation is represented by the power of the highest order derivative in the given differential equation.

In this equation, the order of the differential eq. is $1$ and degree of the differential eq. is $1.$