Question

Degree and order of differential equation $y=x\frac{dy}{dx}+m\sqrt{1+{\left(\frac{dy}{dx}\right)}^2}$ respectively are

• A. $2,1$
• B. $1,2$
• C. $4,2$
• D. $notdefined$

Answer 1

The correct option is A $2,1$

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

$\Rightarrow \left(y-\frac{xdy}{dx}\right)=m\sqrt{1+{\left(\frac{dy}{dx}\right)}^2}$

Squaring both sides we get,

$\Rightarrow y^2+x^2{\left(\frac{dy}{dx}\right)}^2-2xy\frac{dy}{dx}=m^2\left(1+{\left(\frac{dy}{dx}\right)}^2\right)$

$\Rightarrow y^2+\left(x^2-m^2\right){\left(\frac{dy}{dx}\right)}^2-2xy\frac{dy}{dx}-m^2=0$

The order is the highest derivative of differentiation, therefore, the order is $1$.

and degree is power raised to the highest differentiation

Hence, degree is $2$.

$order=1,degree=2$