Question

The order and degree of the differential equation
$\frac{y-x\frac{dy}{dx}}{\frac{dy}{dx}}={\left(\frac{dy}{dx}\right)}^2$ are ____ and _____ respectively.

Answer 1

Order of differential equation is the order of the highest order derivative term present in the differential equation.
Degree of the differential equation is power of that highest order derivative term.

Lets take the given differential equation
$\frac{y-x\frac{dy}{dx}}{\frac{dy}{dx}}={\left(\frac{dy}{dx}\right)}^2$
$\Rightarrow y-x\frac{dy}{dx}={\left(\frac{dy}{dx}\right)}^3$

The highest order derivative term present is $\frac{dy}{dx}$.
$\Rightarrow$ order is $1$.
And the degree of the given differential equation is $3$.