Question

The order and degree of the differential equation ${\left(\frac{dy}{dx}\right)}^2+x=\frac{dx}{dy}+x^2$ are:

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

Answer 1

The correct option is D $1,3$

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

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

$\Rightarrow {\left(\frac{dy}{dx}\right)}^3+(x-x^2)\frac{dy}{dx}-1=0$

So degree of above differential equation is $3$ and order is $1$