Question

The degree of the differential equation $x=1+\left(\frac{dy}{dx}\right)+\frac{1}{2!}{\left(\frac{dy}{dx}\right)}^2+\frac{1}{3!}{\left(\frac{dy}{dx}\right)}^3+...$ is

• A. $1$
• B. $2$
• C. $3$
• D. Not defined

Answer 1

The correct option is A $1$

$x=1+\frac{dy}{dx}+\frac{1}{2!}\left(\frac{dy}{dx}\right)+\frac{1}{3!}\left(\frac{dy}{dx}\right)+....$

$\Rightarrow x=e^{\frac{dy}{dx}}$

$\Rightarrow \log x=\frac{dy}{dx}$

Clearly, it is a differential equation of degree $1$.