Question

The order and degree of the differential equation
$y=x\frac{dy}{dx}+\frac{2}{\left(\frac{dy}{dx}\right)}$ is.

• A. $1,3$
• B. $1,1$
• C. $1,2$
• D. $2,1$

Answer 1

The correct option is C $1,2$

We have, $y=x\frac{dy}{dx}+\frac{2}{\left(\frac{dy}{dx}\right)}$

Multiply both sides by $\frac{dy}{dx}$

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

Clearly above equation polynomial in $\frac{dy}{dx}$

Thus order is highest differential which is $1$

and degree is power to the highest differential which is $2$