Question

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

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

Answer 1

The correct option is C $1$

Given, $=1+\left(\frac{dy}{dx}\right)+\frac{1}{2!}{\left(\frac{dy}{dx}\right)}^2+\frac{1}{3!}{\left(\frac{dy}{dx}\right)}^3+....$
$x=e^{\frac{dy}{dx}}$
$\Rightarrow \frac{dy}{dx}={\log }_{e}x$
Hence the degree of the above differential equation is $1$